subject:(ordinary differential equations)

University of the Western Cape

1. Sheikh, T.O. The role of visualization in the teaching and learning of multivariate calculus and systems of ordinary differential equations .

Degree: 2015, University of the Western Cape

URL: http://hdl.handle.net/11394/5184

► The purpose of this study was to investigate the role of visualization in the conceptualisation and solution of problems in multivariate calculus and dynamical systems.… (more)

▼ The purpose of this study was to investigate the role of visualization in the conceptualisation and solution of problems in multivariate calculus and dynamical systems. The theoretical basis, and the visual and analytical aspects of evaluating multiple integrals, and the stability analysis of dynamical systems, were established. To address the research questions, a teaching experiment with activities to facilitate visualization of 3D objects and phase portraits of non-linear dynamic systems was conducted with an experimental class (n = 24) which received six activity sessions in the computer Laboratory in addition to traditional lectures. The control class (n = 26) received traditional lectures and tutorial instruction. Both groups were lectured by the researcher using the same set of class notes, assignments, worksheets and tutorials. Additional support materials were posted on the Blackboard on Web-City. The activities included tasks in the computer laboratory that reinforced visualization and spatial ability factors such as surface features, nets, projections, cross-sections and rotation of 3D objects as well as phase portraits of systems of differential equations. The students were tested at several time points, and over both the short and long term to assess the impact on their visual and analytical solutions to problems in the two study domains. The pre-test on prior knowledge indicated no significant differences between the means of the experimental and control groups. Results indicate that there were no significant differences between the achievement of the two groups in Test 1 and Test 2 while the activities were ongoing, but towards the end of the semester significant differences in favour of the experimental group were recorded. A multiple linear regression analysis confirmed that in addition to prior knowledge as measured by the pretest, two of the spatial factors were significant predictors of achievement for the domains under investigation. Students had difficulties in visualising 3D regions of integration and in switching the order of triple integrals. Very few (18%) recognised the need for split integrals to span the required area or volume. While students could find analytical solutions to systems of differential equations and describe the stability of individual equilibrium points using eigenvalues, they struggled with translating rates of change into slopes on the phase portraits, with the interpretation of the solutions and in describing the global behaviour of the system. Students had difficulties in visualizing the region of integration in R³, the stability of equilibrium points in the phase portraits, and in coordinating the treatments and conversions between the geometric, numerical, symbolic and algebraic registers. The tendency to work in the algebraic register to determine the limits of the integral was noted, and students opted to use analytic methods in conducting a stability analysis of the given dynamic system rather than the geometric method. This study adds to research on… Advisors/Committee Members: Fray, R (advisor), Benyah, F (advisor).

Subjects/Keywords: Visualization; Multivariate calculus; Mathematics; Ordinary differential equations

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APA (6^th Edition):

Sheikh, T. O. (2015). The role of visualization in the teaching and learning of multivariate calculus and systems of ordinary differential equations . (Thesis). University of the Western Cape. Retrieved from http://hdl.handle.net/11394/5184

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Sheikh, T O. “The role of visualization in the teaching and learning of multivariate calculus and systems of ordinary differential equations .” 2015. Thesis, University of the Western Cape. Accessed March 01, 2021. http://hdl.handle.net/11394/5184.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Sheikh, T O. “The role of visualization in the teaching and learning of multivariate calculus and systems of ordinary differential equations .” 2015. Web. 01 Mar 2021.

Vancouver:

Sheikh TO. The role of visualization in the teaching and learning of multivariate calculus and systems of ordinary differential equations . [Internet] [Thesis]. University of the Western Cape; 2015. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/11394/5184.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sheikh TO. The role of visualization in the teaching and learning of multivariate calculus and systems of ordinary differential equations . [Thesis]. University of the Western Cape; 2015. Available from: http://hdl.handle.net/11394/5184

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

2. Erwin, Samantha H. Mathematical Models of Immune Responses to Infectious Diseases.

Degree: PhD, Mathematics, 2017, Virginia Tech

URL: http://hdl.handle.net/10919/77026

► In this dissertation, we investigate the mechanisms behind diseases and the immune responses required for successful disease resolution in three projects: i) A study of… (more)

Subjects/Keywords: Mathematical biology; theoretical immunology; ordinary differential equations

14 more images…

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APA (6^th Edition):

Erwin, S. H. (2017). Mathematical Models of Immune Responses to Infectious Diseases. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/77026

Chicago Manual of Style (16^th Edition):

Erwin, Samantha H. “Mathematical Models of Immune Responses to Infectious Diseases.” 2017. Doctoral Dissertation, Virginia Tech. Accessed March 01, 2021. http://hdl.handle.net/10919/77026.

MLA Handbook (7^th Edition):

Erwin, Samantha H. “Mathematical Models of Immune Responses to Infectious Diseases.” 2017. Web. 01 Mar 2021.

Vancouver:

Erwin SH. Mathematical Models of Immune Responses to Infectious Diseases. [Internet] [Doctoral dissertation]. Virginia Tech; 2017. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/10919/77026.

Council of Science Editors:

Erwin SH. Mathematical Models of Immune Responses to Infectious Diseases. [Doctoral Dissertation]. Virginia Tech; 2017. Available from: http://hdl.handle.net/10919/77026

3. Lim, Hyun. A Study of Time Decomposition Method for the Semilinear Wave Equations.

Degree: MS, Mathematics and Statistics, 2015, South Dakota State University

URL: https://openprairie.sdstate.edu/etd/1811

► For certain formulations of partial differential equations, proper time-parallel pre conditioners can be successfully applied in space-time finite element simulations. Such an approach may… (more)

Subjects/Keywords: Mathematics; Ordinary Differential Equations and Applied Dynamics

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APA (6^th Edition):

Lim, H. (2015). A Study of Time Decomposition Method for the Semilinear Wave Equations. (Masters Thesis). South Dakota State University. Retrieved from https://openprairie.sdstate.edu/etd/1811

Chicago Manual of Style (16^th Edition):

Lim, Hyun. “A Study of Time Decomposition Method for the Semilinear Wave Equations.” 2015. Masters Thesis, South Dakota State University. Accessed March 01, 2021. https://openprairie.sdstate.edu/etd/1811.

MLA Handbook (7^th Edition):

Lim, Hyun. “A Study of Time Decomposition Method for the Semilinear Wave Equations.” 2015. Web. 01 Mar 2021.

Vancouver:

Lim H. A Study of Time Decomposition Method for the Semilinear Wave Equations. [Internet] [Masters thesis]. South Dakota State University; 2015. [cited 2021 Mar 01]. Available from: https://openprairie.sdstate.edu/etd/1811.

Council of Science Editors:

Lim H. A Study of Time Decomposition Method for the Semilinear Wave Equations. [Masters Thesis]. South Dakota State University; 2015. Available from: https://openprairie.sdstate.edu/etd/1811

University of Pretoria

4. Lee, Wha-Suck. An algebraic - analytic framework for the study of intertwined families of evolution operators.

Degree: Mathematics and Applied Mathematics, 2015, University of Pretoria

URL: http://hdl.handle.net/2263/43532

► We introduce a new framework of generalized operators to handle vector valued distributions, intertwined evolution operators of B-evolution equations and Fokker Planck type evolution equations.… (more)

Subjects/Keywords: B-evolution Equations; Partial Differential Equations; Linear Ordinary Differential Equations in Banach Spaces; UCTD

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APA (6^th Edition):

Lee, W. (2015). An algebraic - analytic framework for the study of intertwined families of evolution operators. (Doctoral Dissertation). University of Pretoria. Retrieved from http://hdl.handle.net/2263/43532

Chicago Manual of Style (16^th Edition):

Lee, Wha-Suck. “An algebraic - analytic framework for the study of intertwined families of evolution operators.” 2015. Doctoral Dissertation, University of Pretoria. Accessed March 01, 2021. http://hdl.handle.net/2263/43532.

MLA Handbook (7^th Edition):

Lee, Wha-Suck. “An algebraic - analytic framework for the study of intertwined families of evolution operators.” 2015. Web. 01 Mar 2021.

Vancouver:

Lee W. An algebraic - analytic framework for the study of intertwined families of evolution operators. [Internet] [Doctoral dissertation]. University of Pretoria; 2015. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/2263/43532.

Council of Science Editors:

Lee W. An algebraic - analytic framework for the study of intertwined families of evolution operators. [Doctoral Dissertation]. University of Pretoria; 2015. Available from: http://hdl.handle.net/2263/43532

Baylor University

5. Lyons, Jeffrey W. Boundary data smoothness for solutions of nonlocal boundary value problems.

Degree: PhD, Mathematics., 2011, Baylor University

URL: http://hdl.handle.net/2104/8153

► In this dissertation, we investigate boundary data smoothness for solutions of nonlocal boundary value problems over discrete and continuous domains. Essentially, we show that under… (more)

Subjects/Keywords: Ordinary differential equations.; Difference equations.; Nonlocal boundary value problem.

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APA (6^th Edition):

Lyons, J. W. (2011). Boundary data smoothness for solutions of nonlocal boundary value problems. (Doctoral Dissertation). Baylor University. Retrieved from http://hdl.handle.net/2104/8153

Chicago Manual of Style (16^th Edition):

Lyons, Jeffrey W. “Boundary data smoothness for solutions of nonlocal boundary value problems.” 2011. Doctoral Dissertation, Baylor University. Accessed March 01, 2021. http://hdl.handle.net/2104/8153.

MLA Handbook (7^th Edition):

Lyons, Jeffrey W. “Boundary data smoothness for solutions of nonlocal boundary value problems.” 2011. Web. 01 Mar 2021.

Vancouver:

Lyons JW. Boundary data smoothness for solutions of nonlocal boundary value problems. [Internet] [Doctoral dissertation]. Baylor University; 2011. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/2104/8153.

Council of Science Editors:

Lyons JW. Boundary data smoothness for solutions of nonlocal boundary value problems. [Doctoral Dissertation]. Baylor University; 2011. Available from: http://hdl.handle.net/2104/8153

Virginia Commonwealth University

6. Ospanov, Asset. DELAY DIFFERENTIAL EQUATIONS AND THEIR APPLICATION TO MICRO ELECTRO MECHANICAL SYSTEMS.

Degree: MS, Mathematical Sciences, 2018, Virginia Commonwealth University

URL: https://doi.org/10.25772/DSAJ-R866 ; https://scholarscompass.vcu.edu/etd/5674

► Delay differential equations have a wide range of applications in engineering. This work is devoted to the analysis of delay Duffing equation, which plays… (more)

Subjects/Keywords: Delay Differential Equations; Periodic Solutions; Dynamic Systems; Ordinary Differential Equations and Applied Dynamics

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APA (6^th Edition):

Ospanov, A. (2018). DELAY DIFFERENTIAL EQUATIONS AND THEIR APPLICATION TO MICRO ELECTRO MECHANICAL SYSTEMS. (Thesis). Virginia Commonwealth University. Retrieved from https://doi.org/10.25772/DSAJ-R866 ; https://scholarscompass.vcu.edu/etd/5674

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ospanov, Asset. “DELAY DIFFERENTIAL EQUATIONS AND THEIR APPLICATION TO MICRO ELECTRO MECHANICAL SYSTEMS.” 2018. Thesis, Virginia Commonwealth University. Accessed March 01, 2021. https://doi.org/10.25772/DSAJ-R866 ; https://scholarscompass.vcu.edu/etd/5674.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ospanov, Asset. “DELAY DIFFERENTIAL EQUATIONS AND THEIR APPLICATION TO MICRO ELECTRO MECHANICAL SYSTEMS.” 2018. Web. 01 Mar 2021.

Vancouver:

Ospanov A. DELAY DIFFERENTIAL EQUATIONS AND THEIR APPLICATION TO MICRO ELECTRO MECHANICAL SYSTEMS. [Internet] [Thesis]. Virginia Commonwealth University; 2018. [cited 2021 Mar 01]. Available from: https://doi.org/10.25772/DSAJ-R866 ; https://scholarscompass.vcu.edu/etd/5674.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ospanov A. DELAY DIFFERENTIAL EQUATIONS AND THEIR APPLICATION TO MICRO ELECTRO MECHANICAL SYSTEMS. [Thesis]. Virginia Commonwealth University; 2018. Available from: https://doi.org/10.25772/DSAJ-R866 ; https://scholarscompass.vcu.edu/etd/5674

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Virginia Commonwealth University

7. Torres, Marcella. A Comparison of Obesity Interventions Using Energy Balance Models.

Degree: MS, Mathematical Sciences, 2015, Virginia Commonwealth University

URL: https://doi.org/10.25772/WSZJ-JM84 ; https://scholarscompass.vcu.edu/etd/3927

► An energy balance model of human metabolism developed by Hall et al. is extended to compare body composition outcomes among standard and proposed obesity… (more)

Subjects/Keywords: metabolism; body composition; differential equations; energy balance; obesity; Ordinary Differential Equations and Applied Dynamics

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APA (6^th Edition):

Torres, M. (2015). A Comparison of Obesity Interventions Using Energy Balance Models. (Thesis). Virginia Commonwealth University. Retrieved from https://doi.org/10.25772/WSZJ-JM84 ; https://scholarscompass.vcu.edu/etd/3927

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Torres, Marcella. “A Comparison of Obesity Interventions Using Energy Balance Models.” 2015. Thesis, Virginia Commonwealth University. Accessed March 01, 2021. https://doi.org/10.25772/WSZJ-JM84 ; https://scholarscompass.vcu.edu/etd/3927.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Torres, Marcella. “A Comparison of Obesity Interventions Using Energy Balance Models.” 2015. Web. 01 Mar 2021.

Vancouver:

Torres M. A Comparison of Obesity Interventions Using Energy Balance Models. [Internet] [Thesis]. Virginia Commonwealth University; 2015. [cited 2021 Mar 01]. Available from: https://doi.org/10.25772/WSZJ-JM84 ; https://scholarscompass.vcu.edu/etd/3927.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Torres M. A Comparison of Obesity Interventions Using Energy Balance Models. [Thesis]. Virginia Commonwealth University; 2015. Available from: https://doi.org/10.25772/WSZJ-JM84 ; https://scholarscompass.vcu.edu/etd/3927

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Oxford

8. Townsend, Alex. Computing with functions in two dimensions.

Degree: PhD, 2014, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:02f92917-809e-477d-8413-417bb8106e56 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627883

► New numerical methods are proposed for computing with smooth scalar and vector valued functions of two variables defined on rectangular domains. Functions are approximated to… (more)

Subjects/Keywords: 515; Mathematics; Numerical analysis; Ordinary differential equations; Partial differential equations; Chebyshev; Chebfun; low rank

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APA (6^th Edition):

Townsend, A. (2014). Computing with functions in two dimensions. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:02f92917-809e-477d-8413-417bb8106e56 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627883

Chicago Manual of Style (16^th Edition):

Townsend, Alex. “Computing with functions in two dimensions.” 2014. Doctoral Dissertation, University of Oxford. Accessed March 01, 2021. http://ora.ox.ac.uk/objects/uuid:02f92917-809e-477d-8413-417bb8106e56 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627883.

MLA Handbook (7^th Edition):

Townsend, Alex. “Computing with functions in two dimensions.” 2014. Web. 01 Mar 2021.

Vancouver:

Townsend A. Computing with functions in two dimensions. [Internet] [Doctoral dissertation]. University of Oxford; 2014. [cited 2021 Mar 01]. Available from: http://ora.ox.ac.uk/objects/uuid:02f92917-809e-477d-8413-417bb8106e56 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627883.

Council of Science Editors:

Townsend A. Computing with functions in two dimensions. [Doctoral Dissertation]. University of Oxford; 2014. Available from: http://ora.ox.ac.uk/objects/uuid:02f92917-809e-477d-8413-417bb8106e56 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627883

University of Toronto

9. Calver, Jonathan Joseph. Parameter Estimation for Systems of Ordinary Differential Equations.

Degree: PhD, 2019, University of Toronto

URL: http://hdl.handle.net/1807/95761

► We consider the formulation and solution of the inverse problem that arises when fit- ting systems of ordinary differential equations (ODEs) to observed data. This… (more)

Subjects/Keywords: Delay Differential Equations; Inverse Problems; Ordinary Differential Equations; Parameter Estimation; Sensitivities; 0984

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APA (6^th Edition):

Calver, J. J. (2019). Parameter Estimation for Systems of Ordinary Differential Equations. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/95761

Chicago Manual of Style (16^th Edition):

Calver, Jonathan Joseph. “Parameter Estimation for Systems of Ordinary Differential Equations.” 2019. Doctoral Dissertation, University of Toronto. Accessed March 01, 2021. http://hdl.handle.net/1807/95761.

MLA Handbook (7^th Edition):

Calver, Jonathan Joseph. “Parameter Estimation for Systems of Ordinary Differential Equations.” 2019. Web. 01 Mar 2021.

Vancouver:

Calver JJ. Parameter Estimation for Systems of Ordinary Differential Equations. [Internet] [Doctoral dissertation]. University of Toronto; 2019. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/1807/95761.

Council of Science Editors:

Calver JJ. Parameter Estimation for Systems of Ordinary Differential Equations. [Doctoral Dissertation]. University of Toronto; 2019. Available from: http://hdl.handle.net/1807/95761

Universidade Federal de Mato Grosso do Sul

10. Moraes, Weslen Xavier de. Solução em série de potencias para equações diferenciais ordinárias lineares de segunda ordem .

Degree: 2016, Universidade Federal de Mato Grosso do Sul

URL: http://repositorio.cbc.ufms.br:8080/jspui/handle/123456789/2885

► Este trabalho trata dos conhecimentos b asicos e intermedi arios sobre equa c~oes diferenciais ordin arias (EDO) at e a segunda ordem. Para solu c~oes… (more)

Subjects/Keywords: Equações Diferenciais Ordinárias; Matemática; Ordinary Differential Equations; Mathematics

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APA (6^th Edition):

Moraes, W. X. d. (2016). Solução em série de potencias para equações diferenciais ordinárias lineares de segunda ordem . (Thesis). Universidade Federal de Mato Grosso do Sul. Retrieved from http://repositorio.cbc.ufms.br:8080/jspui/handle/123456789/2885

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Moraes, Weslen Xavier de. “Solução em série de potencias para equações diferenciais ordinárias lineares de segunda ordem .” 2016. Thesis, Universidade Federal de Mato Grosso do Sul. Accessed March 01, 2021. http://repositorio.cbc.ufms.br:8080/jspui/handle/123456789/2885.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Moraes, Weslen Xavier de. “Solução em série de potencias para equações diferenciais ordinárias lineares de segunda ordem .” 2016. Web. 01 Mar 2021.

Vancouver:

Moraes WXd. Solução em série de potencias para equações diferenciais ordinárias lineares de segunda ordem . [Internet] [Thesis]. Universidade Federal de Mato Grosso do Sul; 2016. [cited 2021 Mar 01]. Available from: http://repositorio.cbc.ufms.br:8080/jspui/handle/123456789/2885.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Moraes WXd. Solução em série de potencias para equações diferenciais ordinárias lineares de segunda ordem . [Thesis]. Universidade Federal de Mato Grosso do Sul; 2016. Available from: http://repositorio.cbc.ufms.br:8080/jspui/handle/123456789/2885

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

UCLA

11. Lewkiewicz, Stephanie Marissa. Mathematical Models of T-cell Population Dynamics in Aging and Immune Disease.

Degree: Mathematics, 2018, UCLA

URL: http://www.escholarship.org/uc/item/4047m652

► In this dissertation, we use birth-death-immigration systems of ordinary differential equations to study the dynamics of human naive T-cell populations in healthy aging and disease… (more)

▼ In this dissertation, we use birth-death-immigration systems of ordinary differential equations to study the dynamics of human naive T-cell populations in healthy aging and disease of the immune system. We derive a model that tracks both total cell counts and counts of clones (groups of genetically identical cells) of a particular size; from the latter, we compute the total clone count, or ``diversity", which provides a quantitative measure of the extent to which the T-cell pool can cope with invading pathogens. We first formulate a nonautonomous model of T-cell birth and replenishment throughout an individual's lifetime, and use it to assess the relationship between the immune tissue damage, T-cell loss and dysfunction, and weakened immune response all observed simultaneously in aging. We identify tissue loss in the thymus as a fundamental cause of diminished T-cell counts, and also that diversity loss can only underlie weakened immune effectiveness in aging if small clones are ineffective against pathogen. Using a short-time, autonomous version of the same ODE, we then study changes to the T-cell pool during an instance of acute thymic atrophy and recovery. We identify equilibrium solutions that arise at different rates of T-cell production, and derive analytic approximations to the eigenvalues and eigenvectors of the linearization around the equilibria. From the forms of the eigenvalues and eigenvectors, we are able to estimate rates at which different size-segregated groups of clones converge to equilibria – that is, ``adjust" to the changing rate of T-cell production. Finally, we formulate a total cell count model of populations of HIV-immune and HIV-susceptible cells of the T-cell lineage in the bone marrow, thymus, and peripheral blood after transplant of HIV-immune bone marrow into an HIV-infected individual. We show that independent of assumptions about the homeostatic mechanism in the periphery, the ratio of HIV-immune to HIV-susceptible T-cells in each immune region should asymptotically approach the ratio of HIV-immune to HIV-susceptible stem cells that results after bone marrow transplant with no infection present. We show that with virus introduced into the system, the asymptotic ratio of HIV-immune to HIV-susceptible peripheral T-cells is highly sensitive to parameters affecting the body's ability to clear the virus.

Subjects/Keywords: Applied mathematics; Mathematics; immunology; mathematical biology; ordinary differential equations; population dynamics

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APA (6^th Edition):

Lewkiewicz, S. M. (2018). Mathematical Models of T-cell Population Dynamics in Aging and Immune Disease. (Thesis). UCLA. Retrieved from http://www.escholarship.org/uc/item/4047m652

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Lewkiewicz, Stephanie Marissa. “Mathematical Models of T-cell Population Dynamics in Aging and Immune Disease.” 2018. Thesis, UCLA. Accessed March 01, 2021. http://www.escholarship.org/uc/item/4047m652.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Lewkiewicz, Stephanie Marissa. “Mathematical Models of T-cell Population Dynamics in Aging and Immune Disease.” 2018. Web. 01 Mar 2021.

Vancouver:

Lewkiewicz SM. Mathematical Models of T-cell Population Dynamics in Aging and Immune Disease. [Internet] [Thesis]. UCLA; 2018. [cited 2021 Mar 01]. Available from: http://www.escholarship.org/uc/item/4047m652.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lewkiewicz SM. Mathematical Models of T-cell Population Dynamics in Aging and Immune Disease. [Thesis]. UCLA; 2018. Available from: http://www.escholarship.org/uc/item/4047m652

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Texas A&M University

12. Ng, Chee Loong. Parameter estimation in ordinary differential equations.

Degree: MS, Computer Science, 2004, Texas A&M University

URL: http://hdl.handle.net/1969.1/388

► The parameter estimation problem or the inverse problem of ordinary differential equations is prevalent in many process models in chemistry, molecular biology, control system design… (more)

Subjects/Keywords: Parameter; Estimation; Ordinary Differential Equations

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APA (6^th Edition):

Ng, C. L. (2004). Parameter estimation in ordinary differential equations. (Masters Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/388

Chicago Manual of Style (16^th Edition):

Ng, Chee Loong. “Parameter estimation in ordinary differential equations.” 2004. Masters Thesis, Texas A&M University. Accessed March 01, 2021. http://hdl.handle.net/1969.1/388.

MLA Handbook (7^th Edition):

Ng, Chee Loong. “Parameter estimation in ordinary differential equations.” 2004. Web. 01 Mar 2021.

Vancouver:

Ng CL. Parameter estimation in ordinary differential equations. [Internet] [Masters thesis]. Texas A&M University; 2004. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/1969.1/388.

Council of Science Editors:

Ng CL. Parameter estimation in ordinary differential equations. [Masters Thesis]. Texas A&M University; 2004. Available from: http://hdl.handle.net/1969.1/388

University of Waterloo

13. Dockhorn, Tim. Generative Modeling with Neural Ordinary Differential Equations.

Degree: 2019, University of Waterloo

URL: http://hdl.handle.net/10012/15354

► Neural ordinary differential equations (NODEs) (Chen et al., 2018) are ordinary differential equations (ODEs) with their dynamics modeled by neural networks. Continuous normalizing flows (CNFs)… (more)

Subjects/Keywords: generative modeling; neural ordinary differential equations; density estimation; deep learning

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APA (6^th Edition):

Dockhorn, T. (2019). Generative Modeling with Neural Ordinary Differential Equations. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/15354

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Dockhorn, Tim. “Generative Modeling with Neural Ordinary Differential Equations.” 2019. Thesis, University of Waterloo. Accessed March 01, 2021. http://hdl.handle.net/10012/15354.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Dockhorn, Tim. “Generative Modeling with Neural Ordinary Differential Equations.” 2019. Web. 01 Mar 2021.

Vancouver:

Dockhorn T. Generative Modeling with Neural Ordinary Differential Equations. [Internet] [Thesis]. University of Waterloo; 2019. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/10012/15354.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Dockhorn T. Generative Modeling with Neural Ordinary Differential Equations. [Thesis]. University of Waterloo; 2019. Available from: http://hdl.handle.net/10012/15354

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

14. Gudla, Pradeep K. High-order multistep asynchronous splitting methods (MASM) for the numerical solution of multiple-time-scale ordinary differential equations.

Degree: PhD, Mechanical Engineering, 2016, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/90556

► Often one encounters dynamical systems containing a wide range of natural frequencies. These multiple-time-scale systems, which are modeled using stiff ordinary differential equations, are well… (more)

▼ Often one encounters dynamical systems containing a wide range of natural frequencies. These multiple-time-scale systems, which are modeled using stiff ordinary differential equations, are well known to present a significant challenge in obtaining a numerical solution efficiently. Multiple-time-scale systems can be broadly classified into two classes: (1) systems with well-separate discrete time scales, such as molecular dynamic simulations and electrical networks, and (2) systems with a continuously-distributed range of time scales, such as aerosol dynamics, multiscale structural dynamics and turbulent fluid flow. For the numerical simulation of systems with well-separated discrete time scales one can frequently average over the fast time scales, either analytically or numerically. This results in effective models with only slower time scales and allows efficient numerical simulations with large timesteps. In cases where this is not possible, either due to system complexity or the fact that there is simply a wide range of timescales with no clear scale separation, such as the continuously-distributed time scales systems, it has traditionally been necessary to simulate the entire system at the rate of the fastest timescale, which can be very expensive. To efficiently simulate multiple-time-scale systems, many researchers have developed multiple-time-step numerical integration methods, where more than one timestep are used. These advance different components of the system forward in time at different rates, so that faster components can use small timesteps, while slower components can use large timesteps, resulting in lower computational cost. Most multiple-time-step integrators only apply to systems with discrete time scales, where subcycling methods, mollified methods, and r-RESPA are good examples. In addition, these methods which have several numerical timesteps require that timestep ratios be integer multiples of each other. In contrast, one family of multiple-time-step methods does not attempt to enforce any such restrictions, namely asynchronous integrators. These methods have incommensurate timesteps, such that all system components never synchronize at common time instants. This feature allows some asynchronous methods to be efficiently applied to systems with continuously-distributed time scales, where every time scale can have an appropriately-chosen numeral timestep. However, currently known asynchronous methods are at most second-order accurate and are known to suffer from resonance instabilities, severely limiting their practical efficiency gain relative to their synchronous counterparts. In the present work, a new family of high-order Multistep Asynchronous Splitting Methods (MASM) is developed, based on a generalization of both classical linear multistep methods and the previously-known Asynchronous Splitting Methods (ASMs). These new methods compute high-order trajectory approximations using the history of system states and force vectors as for linear multistep methods, while at the same time… Advisors/Committee Members: West, Matthew (advisor), West, Matthew (Committee Chair), Salapaka, Srinivasa (committee member), Dullerud, Geir (committee member), Vakakis, Alexander (committee member), Kloeckner, Andreas (committee member).

Subjects/Keywords: Stiff Ordinary Differential Equations

…List of Abbreviations ODE Ordinary Differential Equations. MASM Multistep based… …methods. We will consider systems of first-order ordinary differential equations (ODEs)… …x28;m) mth order time differential of force vector δtotal Cost of simulation due to… …full aerosol condensation equations are complicated implicit functions of the rates, so…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gudla, P. K. (2016). High-order multistep asynchronous splitting methods (MASM) for the numerical solution of multiple-time-scale ordinary differential equations. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/90556

Chicago Manual of Style (16^th Edition):

Gudla, Pradeep K. “High-order multistep asynchronous splitting methods (MASM) for the numerical solution of multiple-time-scale ordinary differential equations.” 2016. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed March 01, 2021. http://hdl.handle.net/2142/90556.

MLA Handbook (7^th Edition):

Gudla, Pradeep K. “High-order multistep asynchronous splitting methods (MASM) for the numerical solution of multiple-time-scale ordinary differential equations.” 2016. Web. 01 Mar 2021.

Vancouver:

Gudla PK. High-order multistep asynchronous splitting methods (MASM) for the numerical solution of multiple-time-scale ordinary differential equations. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2016. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/2142/90556.

Council of Science Editors:

Gudla PK. High-order multistep asynchronous splitting methods (MASM) for the numerical solution of multiple-time-scale ordinary differential equations. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2016. Available from: http://hdl.handle.net/2142/90556

Université Catholique de Louvain

15. Jaeger, Jonathan. Functional estimation in systems defined by differential equations using Bayesian smoothing methods.

Degree: 2012, Université Catholique de Louvain

URL: http://hdl.handle.net/2078.1/115164

►

Ordinary differential equations (ODEs) are widely used to model physical, chemical and biological processes. Currently, the most commonly used estimation procedures rely on nonlinear least… (more)

▼

Ordinary differential equations (ODEs) are widely used to model physical, chemical and biological processes. Currently, the most commonly used estimation procedures rely on nonlinear least squares. It uses minimization techniques for the estimation of the ODE parameters and a numerical solver for the approximation of the solution. These approaches are computationally intensive and often poorly suited for statistical inference. Recently, a penalized smoothing method was introduced for parameter estimation and approximation of the solution of systems of differential equations. This approach requires an approximation of the state functions involved in the system of differential equations and a penalty term based on all of these equations. It has solved some of the problems encountered in conventional approaches but suffers from two weaknesses: the selection of the ODE-adhesion parameters is not automatic and the uncertainty measures on the estimation of the ODE parameters must be approximated. This thesis proposes to adapt this ODE-penalized smoothing approach in a Bayesian framework for systems of affine differential equations when the data distribution is homogeneous. The two main disadvantages of the frequentist approach are overcome in the Bayesian framework: the selection of the ODE-adhesion parameters is now automatic and the uncertainty measures about parameters can be easily obtained using a sample from the joint posterior distribution. In addition, in this Bayesian approach, prior information about the ODE parameters can be introduced. It manages also in natural way multi-subject studies. Finally, the ODE-adhesion parameters related to each differential equation of the system can be used to validate the proposed dynamic model. The selection of a dynamic model among several alternatives can be obtained by the comparison of the posterior distributions for these ODE-adhesion parameters.

(STAT 3) – UCL, 2012

Advisors/Committee Members: UCL - SSH/IMMAQ/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles, Lambert, Philippe, Von Sachs, Rainer, Legrand, Catherine, Govaerts, Bernadette, Eilers, Paul.

Subjects/Keywords: Bayesian ODE-penalized B-spline; ODE-model selection; Ordinary differential equations

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APA (6^th Edition):

Jaeger, J. (2012). Functional estimation in systems defined by differential equations using Bayesian smoothing methods. (Thesis). Université Catholique de Louvain. Retrieved from http://hdl.handle.net/2078.1/115164

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Jaeger, Jonathan. “Functional estimation in systems defined by differential equations using Bayesian smoothing methods.” 2012. Thesis, Université Catholique de Louvain. Accessed March 01, 2021. http://hdl.handle.net/2078.1/115164.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Jaeger, Jonathan. “Functional estimation in systems defined by differential equations using Bayesian smoothing methods.” 2012. Web. 01 Mar 2021.

Vancouver:

Jaeger J. Functional estimation in systems defined by differential equations using Bayesian smoothing methods. [Internet] [Thesis]. Université Catholique de Louvain; 2012. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/2078.1/115164.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Jaeger J. Functional estimation in systems defined by differential equations using Bayesian smoothing methods. [Thesis]. Université Catholique de Louvain; 2012. Available from: http://hdl.handle.net/2078.1/115164

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Manchester

16. Yang, Jie. Prediction of combination efficacy in cancer therapy.

Degree: PhD, 2013, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/prediction-of-combination-efficacy-in-cancer-therapy(1b49824b-9d5f-4d21-89d7-6160a810d05e).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.574342

► The cell cycle is an essential process in all living organisms that must be carefully regulated to ensure successful cell growth and division. Disregulation of… (more)

▼ The cell cycle is an essential process in all living organisms that must be carefully regulated to ensure successful cell growth and division. Disregulation of the cell cycle is a key contributing factor towards the formation of cancerous cells. Understanding events at a cellular level is the first step towards comprehending how cancer manifests at an organismal level. Mathematical modelling can be used as a means of formalising and predicting the behaviour of the biological systems involved in cancer. In response, cell cycle models have been constructed to simulate and predict what happens to the mammalian cell over a time course in response to variable parameters.Current cell cycle models rarely account for certain precursors of cell growth such as energy usage and the need for non-essential amino acids as fundamental building blocks of macromolecules. Normal and cancer cell metabolism differ in the way they derive energy from glucose. In addition, normal and cancer cells also demonstrate different levels of gene expression. Two versions of a mammalian cell cycle and metabolism model, based on ordinary differential equations (ODEs) that respond to fluctuations in glucose concentration levels, have been developed here for the normal and cancer cell scenarios. Sensitivity analysis is performed for both normal and cancer cells using these cell cycle and metabolism models to investigate which kinetic reaction steps have a greater effect over the cell cycle period. Detailed analysis of the models and quantitatively assessing metabolite levels at various stages of the cell cycle may offer novel insights into how the glycolytic rate varies during the cell cycle for both normal and cancer cells.The results of the sensitivity analysis are used to identify potential drug targets in cancer therapy. Combinations of these individual targets are also investigated to compare the different effects of single and multiple drug compounds on the time it takes to complete a cell division cycle.

Subjects/Keywords: 616.994; Cell Cycle; Metabolism; Mathematical Modelling; Ordinary Differential Equations; Systems Biology

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APA (6^th Edition):

Yang, J. (2013). Prediction of combination efficacy in cancer therapy. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/prediction-of-combination-efficacy-in-cancer-therapy(1b49824b-9d5f-4d21-89d7-6160a810d05e).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.574342

Chicago Manual of Style (16^th Edition):

Yang, Jie. “Prediction of combination efficacy in cancer therapy.” 2013. Doctoral Dissertation, University of Manchester. Accessed March 01, 2021. https://www.research.manchester.ac.uk/portal/en/theses/prediction-of-combination-efficacy-in-cancer-therapy(1b49824b-9d5f-4d21-89d7-6160a810d05e).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.574342.

MLA Handbook (7^th Edition):

Yang, Jie. “Prediction of combination efficacy in cancer therapy.” 2013. Web. 01 Mar 2021.

Vancouver:

Yang J. Prediction of combination efficacy in cancer therapy. [Internet] [Doctoral dissertation]. University of Manchester; 2013. [cited 2021 Mar 01]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/prediction-of-combination-efficacy-in-cancer-therapy(1b49824b-9d5f-4d21-89d7-6160a810d05e).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.574342.

Council of Science Editors:

Yang J. Prediction of combination efficacy in cancer therapy. [Doctoral Dissertation]. University of Manchester; 2013. Available from: https://www.research.manchester.ac.uk/portal/en/theses/prediction-of-combination-efficacy-in-cancer-therapy(1b49824b-9d5f-4d21-89d7-6160a810d05e).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.574342

University of Newcastle upon Tyne

17. Hermansyah, Edy. An investigation of collocation algorithms for solving boundary value problems system of ODEs.

Degree: PhD, 2001, University of Newcastle upon Tyne

URL: http://theses.ncl.ac.uk/jspui/handle/10443/1976 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366541

► This thesis is concerned with an investigation and evaluation of collocation algorithms for solving two-point boundary value problems for systems of ordinary differential equations. An… (more)

▼ This thesis is concerned with an investigation and evaluation of collocation algorithms for solving two-point boundary value problems for systems of ordinary differential equations. An emphasis is on developing reliable and efficient adaptive mesh selection algorithms in piecewise collocation methods. General background materials including basic concepts and descriptions of the method as well as some functional analysis tools needed in developing some error estimates are given at the beginning. A brief review of some developments in the methods to be used is provided for later referencing. By utilising the special structure of the collocation matrices, a more compact block matrix structure is introduced and an algorithm for generating and solving the matrix is proposed. Some practical aspects and computational considerations of matrices involved in the collocation process such as analysis of arithmetic operations and amount of memory spaces needed are considered. An examination of scaling process to reduce the condition number is also presented. A numerical evaluation of some error estimates developed by considering the differential operator, the related matrices and the residual is carried out. These estimates are used to develop adaptive mesh selection algorithms, in particular as a cheap criterion for terminating the computation process. Following a discussion on mesh selection strategies, a criterion function for use in adaptive algorithms is introduced and a numerical scheme to equidistributing values of the criterion function is proposed. An adaptive algorithm based on this criterion is developed and the results of numerical experiments are compared with those using some well known criterion functions. The various examples are chosen in such a way that they include problems with interior or boundary layers. In addition, an algorithm has been developed to predict the necessary number of subintervals for a given tolerance, with the aim of improving the efficiency of the whole process. Using a good initial mesh in adaptive algorithms would be expected to provide some further improvement in the algorithms. This leads to the idea of locating the layer regions and determining suitable break points in such regions before the numerical process. Based on examining the eigenvalues of the coefficient matrix in the differential equation in the specified interval, using their magnitudes and rates of change, the algorithms for predicting possible layer regions and estimating the number of break points needed in such regions are constructed. The effectiveness of these algorithms is evaluated by carrying out a number of numerical experiments. The final chapter gives some concluding remarks of the work and comment on results of numerical experiments. Certain possible improvements and extensions for further research are also briefly given.

Subjects/Keywords: 519; Ordinary differential equations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Hermansyah, E. (2001). An investigation of collocation algorithms for solving boundary value problems system of ODEs. (Doctoral Dissertation). University of Newcastle upon Tyne. Retrieved from http://theses.ncl.ac.uk/jspui/handle/10443/1976 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366541

Chicago Manual of Style (16^th Edition):

Hermansyah, Edy. “An investigation of collocation algorithms for solving boundary value problems system of ODEs.” 2001. Doctoral Dissertation, University of Newcastle upon Tyne. Accessed March 01, 2021. http://theses.ncl.ac.uk/jspui/handle/10443/1976 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366541.

MLA Handbook (7^th Edition):

Hermansyah, Edy. “An investigation of collocation algorithms for solving boundary value problems system of ODEs.” 2001. Web. 01 Mar 2021.

Vancouver:

Hermansyah E. An investigation of collocation algorithms for solving boundary value problems system of ODEs. [Internet] [Doctoral dissertation]. University of Newcastle upon Tyne; 2001. [cited 2021 Mar 01]. Available from: http://theses.ncl.ac.uk/jspui/handle/10443/1976 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366541.

Council of Science Editors:

Hermansyah E. An investigation of collocation algorithms for solving boundary value problems system of ODEs. [Doctoral Dissertation]. University of Newcastle upon Tyne; 2001. Available from: http://theses.ncl.ac.uk/jspui/handle/10443/1976 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366541

University of New Mexico

18. Dong, Yan. Nonparametric Bayes approach for a semi-mechanistic pharmacokinetic and pharmacodynamic model.

Degree: Mathematics & Statistics, 2015, University of New Mexico

URL: http://hdl.handle.net/1928/27775

► Both frequentist and Bayesian approaches have been used to characterize population pharmacokinetics and pharmacodynamics(PK/PD) models. These methods focus on estimating the population parameters and assessing… (more)

Subjects/Keywords: Dirichlet ProcessProcess; Nonparametric Bayes; Pharmacokinetics; Pharmacodynamics; Ordinary differential equations

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APA (6^th Edition):

Dong, Y. (2015). Nonparametric Bayes approach for a semi-mechanistic pharmacokinetic and pharmacodynamic model. (Doctoral Dissertation). University of New Mexico. Retrieved from http://hdl.handle.net/1928/27775

Chicago Manual of Style (16^th Edition):

Dong, Yan. “Nonparametric Bayes approach for a semi-mechanistic pharmacokinetic and pharmacodynamic model.” 2015. Doctoral Dissertation, University of New Mexico. Accessed March 01, 2021. http://hdl.handle.net/1928/27775.

MLA Handbook (7^th Edition):

Dong, Yan. “Nonparametric Bayes approach for a semi-mechanistic pharmacokinetic and pharmacodynamic model.” 2015. Web. 01 Mar 2021.

Vancouver:

Dong Y. Nonparametric Bayes approach for a semi-mechanistic pharmacokinetic and pharmacodynamic model. [Internet] [Doctoral dissertation]. University of New Mexico; 2015. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/1928/27775.

Council of Science Editors:

Dong Y. Nonparametric Bayes approach for a semi-mechanistic pharmacokinetic and pharmacodynamic model. [Doctoral Dissertation]. University of New Mexico; 2015. Available from: http://hdl.handle.net/1928/27775

University of Minnesota

19. Meyer, Katherine. Metric Properties of Attractors for Vector Fields via Bounded, Nonautonomous Control.

Degree: PhD, Mathematics, 2019, University of Minnesota

URL: http://hdl.handle.net/11299/206214

► Attractors organize long-term behavior in dynamical systems, and their robustness against perturbations reflects both the resilience of a model system and the likelihood that the… (more)

Subjects/Keywords: attractors; intensity; multiflows; ordinary differential equations; resilience; transient dynamics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Meyer, K. (2019). Metric Properties of Attractors for Vector Fields via Bounded, Nonautonomous Control. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/206214

Chicago Manual of Style (16^th Edition):

Meyer, Katherine. “Metric Properties of Attractors for Vector Fields via Bounded, Nonautonomous Control.” 2019. Doctoral Dissertation, University of Minnesota. Accessed March 01, 2021. http://hdl.handle.net/11299/206214.

MLA Handbook (7^th Edition):

Meyer, Katherine. “Metric Properties of Attractors for Vector Fields via Bounded, Nonautonomous Control.” 2019. Web. 01 Mar 2021.

Vancouver:

Meyer K. Metric Properties of Attractors for Vector Fields via Bounded, Nonautonomous Control. [Internet] [Doctoral dissertation]. University of Minnesota; 2019. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/11299/206214.

Council of Science Editors:

Meyer K. Metric Properties of Attractors for Vector Fields via Bounded, Nonautonomous Control. [Doctoral Dissertation]. University of Minnesota; 2019. Available from: http://hdl.handle.net/11299/206214

University of Tennessee – Knoxville

20. Trask, Jillian M. Modeling Celiac Disease.

Degree: MS, Mathematics, 2014, University of Tennessee – Knoxville

URL: https://trace.tennessee.edu/utk_gradthes/2855

► Those who suffer from Celiac Disease have an autoimmune response to the protein complex gluten. The goal of this work is to better understand… (more)

Subjects/Keywords: celiac; gluten; autoimmune; zonulin; permeability; Ordinary Differential Equations and Applied Dynamics

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APA (6^th Edition):

Trask, J. M. (2014). Modeling Celiac Disease. (Thesis). University of Tennessee – Knoxville. Retrieved from https://trace.tennessee.edu/utk_gradthes/2855

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Trask, Jillian M. “Modeling Celiac Disease.” 2014. Thesis, University of Tennessee – Knoxville. Accessed March 01, 2021. https://trace.tennessee.edu/utk_gradthes/2855.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Trask, Jillian M. “Modeling Celiac Disease.” 2014. Web. 01 Mar 2021.

Vancouver:

Trask JM. Modeling Celiac Disease. [Internet] [Thesis]. University of Tennessee – Knoxville; 2014. [cited 2021 Mar 01]. Available from: https://trace.tennessee.edu/utk_gradthes/2855.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Trask JM. Modeling Celiac Disease. [Thesis]. University of Tennessee – Knoxville; 2014. Available from: https://trace.tennessee.edu/utk_gradthes/2855

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Delft University of Technology

21. Haaker, T.I. Quasi-steady modelling and asymptotic analysis of aeroelastic oscillators.

Degree: 1996, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; urn:NBN:nl:ui:24-uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; urn:NBN:nl:ui:24-uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; http://resolver.tudelft.nl/uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a

Subjects/Keywords: ordinary differential equations; galloping; aeroelasticity

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APA (6^th Edition):

Haaker, T. I. (1996). Quasi-steady modelling and asymptotic analysis of aeroelastic oscillators. (Doctoral Dissertation). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; urn:NBN:nl:ui:24-uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; urn:NBN:nl:ui:24-uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; http://resolver.tudelft.nl/uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a

Chicago Manual of Style (16^th Edition):

Haaker, T I. “Quasi-steady modelling and asymptotic analysis of aeroelastic oscillators.” 1996. Doctoral Dissertation, Delft University of Technology. Accessed March 01, 2021. http://resolver.tudelft.nl/uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; urn:NBN:nl:ui:24-uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; urn:NBN:nl:ui:24-uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; http://resolver.tudelft.nl/uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a.

MLA Handbook (7^th Edition):

Haaker, T I. “Quasi-steady modelling and asymptotic analysis of aeroelastic oscillators.” 1996. Web. 01 Mar 2021.

Vancouver:

Haaker TI. Quasi-steady modelling and asymptotic analysis of aeroelastic oscillators. [Internet] [Doctoral dissertation]. Delft University of Technology; 1996. [cited 2021 Mar 01]. Available from: http://resolver.tudelft.nl/uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; urn:NBN:nl:ui:24-uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; urn:NBN:nl:ui:24-uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; http://resolver.tudelft.nl/uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a.

Council of Science Editors:

Haaker TI. Quasi-steady modelling and asymptotic analysis of aeroelastic oscillators. [Doctoral Dissertation]. Delft University of Technology; 1996. Available from: http://resolver.tudelft.nl/uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; urn:NBN:nl:ui:24-uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; urn:NBN:nl:ui:24-uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a ; http://resolver.tudelft.nl/uuid:f7df944a-9342-41f6-910e-4c9b3e40be6a

University of Ottawa

22. Bolohan, Noah. Seasonal Variation in a Predator-Predator-Prey Model.

Degree: MSc, Sciences / Science, 2020, University of Ottawa

URL: http://dx.doi.org/10.20381/ruor-25125

► Seasonal shifts in predation habits, from a generalist in the summer to a specialist in the winter, have been documented for the great horned owl… (more)

Subjects/Keywords: Population dynamics; Ordinary differential equations; Seasonality; Modelling; Predator prey; Mathematical ecology

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APA (6^th Edition):

Bolohan, N. (2020). Seasonal Variation in a Predator-Predator-Prey Model. (Masters Thesis). University of Ottawa. Retrieved from http://dx.doi.org/10.20381/ruor-25125

Chicago Manual of Style (16^th Edition):

Bolohan, Noah. “Seasonal Variation in a Predator-Predator-Prey Model.” 2020. Masters Thesis, University of Ottawa. Accessed March 01, 2021. http://dx.doi.org/10.20381/ruor-25125.

MLA Handbook (7^th Edition):

Bolohan, Noah. “Seasonal Variation in a Predator-Predator-Prey Model.” 2020. Web. 01 Mar 2021.

Vancouver:

Bolohan N. Seasonal Variation in a Predator-Predator-Prey Model. [Internet] [Masters thesis]. University of Ottawa; 2020. [cited 2021 Mar 01]. Available from: http://dx.doi.org/10.20381/ruor-25125.

Council of Science Editors:

Bolohan N. Seasonal Variation in a Predator-Predator-Prey Model. [Masters Thesis]. University of Ottawa; 2020. Available from: http://dx.doi.org/10.20381/ruor-25125

University of Louisville

23. Riley, Jeremy Warren. Fenichel's theorems with applications in dynamical systems.

Degree: MA, 2012, University of Louisville

URL: 10.18297/etd/1208 ; https://ir.library.louisville.edu/etd/1208

► Three main theorems due to Fenichel are fundamental tools in the exploration of geometric singular perturbation theory. This expository paper attempts to provide an introduction… (more)

Subjects/Keywords: Fenichel's theorems; Math modeling; Dynamical systems; Ordinary differential equations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Riley, J. W. (2012). Fenichel's theorems with applications in dynamical systems. (Masters Thesis). University of Louisville. Retrieved from 10.18297/etd/1208 ; https://ir.library.louisville.edu/etd/1208

Chicago Manual of Style (16^th Edition):

Riley, Jeremy Warren. “Fenichel's theorems with applications in dynamical systems.” 2012. Masters Thesis, University of Louisville. Accessed March 01, 2021. 10.18297/etd/1208 ; https://ir.library.louisville.edu/etd/1208.

MLA Handbook (7^th Edition):

Riley, Jeremy Warren. “Fenichel's theorems with applications in dynamical systems.” 2012. Web. 01 Mar 2021.

Vancouver:

Riley JW. Fenichel's theorems with applications in dynamical systems. [Internet] [Masters thesis]. University of Louisville; 2012. [cited 2021 Mar 01]. Available from: 10.18297/etd/1208 ; https://ir.library.louisville.edu/etd/1208.

Council of Science Editors:

Riley JW. Fenichel's theorems with applications in dynamical systems. [Masters Thesis]. University of Louisville; 2012. Available from: 10.18297/etd/1208 ; https://ir.library.louisville.edu/etd/1208

24. Joshi, Tejas C. A Model of the Appendix's Role in Clostridium difficile Infection.

Degree: MSs, Mathematics, 2017, Case Western Reserve University School of Graduate Studies

URL: http://rave.ohiolink.edu/etdc/view?acc_num=case1492599340909151

► The appendix has been hypothesized to protect the colon against Clostridiumdifficile infection (CDI) by providing a continuous source of commensal bacteriathat crowd out the pathogen… (more)

Subjects/Keywords: Mathematics; Biology; Appendix; Clostridium difficile infection; model; ordinary differential equations; bistability

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APA (6^th Edition):

Joshi, T. C. (2017). A Model of the Appendix's Role in Clostridium difficile Infection. (Masters Thesis). Case Western Reserve University School of Graduate Studies. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=case1492599340909151

Chicago Manual of Style (16^th Edition):

Joshi, Tejas C. “A Model of the Appendix's Role in Clostridium difficile Infection.” 2017. Masters Thesis, Case Western Reserve University School of Graduate Studies. Accessed March 01, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1492599340909151.

MLA Handbook (7^th Edition):

Joshi, Tejas C. “A Model of the Appendix's Role in Clostridium difficile Infection.” 2017. Web. 01 Mar 2021.

Vancouver:

Joshi TC. A Model of the Appendix's Role in Clostridium difficile Infection. [Internet] [Masters thesis]. Case Western Reserve University School of Graduate Studies; 2017. [cited 2021 Mar 01]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=case1492599340909151.

Council of Science Editors:

Joshi TC. A Model of the Appendix's Role in Clostridium difficile Infection. [Masters Thesis]. Case Western Reserve University School of Graduate Studies; 2017. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=case1492599340909151

University of Tennessee – Knoxville

25. Phillips, Tricia Marie. Data-Driven Modeling of the Heroin and Fentanyl Epidemic and the Harvesting of Trees in West Africa.

Degree: 2020, University of Tennessee – Knoxville

URL: https://trace.tennessee.edu/utk_graddiss/5897

► The opioid epidemic has had a strong presence in the United States in recent years. Drug overdose deaths involving opioids have skyrocketed and the lacing… (more)

▼ The opioid epidemic has had a strong presence in the United States in recent years. Drug overdose deaths involving opioids have skyrocketed and the lacing of heroin with fentanyl has played a significant role in this. In order to investigate the dynamics behind the opioid epidemic and predict its trajectory, we formulate a system of ordinary differential equations that incorporate the movement of individuals among classes of opioid use. We estimate parameter values by fitting to Tennessee data since the time the epidemic was established in the state. The trajectory of the epidemic suggests the number of addicts and overdose deaths will increase over the next few years and is driven by the size of the heroin/fentanyl addicted class. We measure the sensitivity of the size of the opioid addicted classes to each of the parameters at the beginning of 2023. From these results, with the hopes of mitigating the increasing trajectory of the epidemic in the near future, management scenarios for decreasing the number of addicted individuals and overdose deaths from 2020-2023 are explored. The most effective include increasing accessibility to treatment programs, monitoring individuals who have stably recovered, and increasing the use of opioid overdose-reversal drugs. Khaya senegalensis is a tree species in Benin, West Africa that is harvested both lethally and non-lethally for its non-timber forest products by the local people for cultural and economic reasons. Both adult and juvenile trees are harvested which affects various vital rates for the tree population. To investigate the effect of size-dependent harvesting strategies on tree population dynamics, we develop a size-structured, seasonal system of difference equations with time-varying harvest for this tree species. Using data from a specific population of the species, the Soassararou population, we estimate harvesting rates and rates affected by harvest for our harvesting model applied to the Soassararou and Nipuni populations. Eigenvalue analysis is then carried out to compare population dynamics.

Subjects/Keywords: opioids; heroin; fentanyl; harvesting; modeling; ordinary differential equations

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APA (6^th Edition):

Phillips, T. M. (2020). Data-Driven Modeling of the Heroin and Fentanyl Epidemic and the Harvesting of Trees in West Africa. (Doctoral Dissertation). University of Tennessee – Knoxville. Retrieved from https://trace.tennessee.edu/utk_graddiss/5897

Chicago Manual of Style (16^th Edition):

Phillips, Tricia Marie. “Data-Driven Modeling of the Heroin and Fentanyl Epidemic and the Harvesting of Trees in West Africa.” 2020. Doctoral Dissertation, University of Tennessee – Knoxville. Accessed March 01, 2021. https://trace.tennessee.edu/utk_graddiss/5897.

MLA Handbook (7^th Edition):

Phillips, Tricia Marie. “Data-Driven Modeling of the Heroin and Fentanyl Epidemic and the Harvesting of Trees in West Africa.” 2020. Web. 01 Mar 2021.

Vancouver:

Phillips TM. Data-Driven Modeling of the Heroin and Fentanyl Epidemic and the Harvesting of Trees in West Africa. [Internet] [Doctoral dissertation]. University of Tennessee – Knoxville; 2020. [cited 2021 Mar 01]. Available from: https://trace.tennessee.edu/utk_graddiss/5897.

Council of Science Editors:

Phillips TM. Data-Driven Modeling of the Heroin and Fentanyl Epidemic and the Harvesting of Trees in West Africa. [Doctoral Dissertation]. University of Tennessee – Knoxville; 2020. Available from: https://trace.tennessee.edu/utk_graddiss/5897

University of Tennessee – Knoxville

26. Ramanan, Lavanya. The Complementing Condition in Elasticity.

Degree: MS, Mathematics, 2014, University of Tennessee – Knoxville

URL: https://trace.tennessee.edu/utk_gradthes/2748

► We consider a boundary value problem of nonlinear elasticity on a domain [omega] in R³ [3-dimensional space] and compute the Complementing Condition for the… (more)

Subjects/Keywords: Elasticity; Boundary Value Problem; Complementing Condition; Deformation; Second-Order Ordinary Differential Equation; Continuum Mechanics; Mathematics; Ordinary Differential Equations and Applied Dynamics

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APA (6^th Edition):

Ramanan, L. (2014). The Complementing Condition in Elasticity. (Thesis). University of Tennessee – Knoxville. Retrieved from https://trace.tennessee.edu/utk_gradthes/2748

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ramanan, Lavanya. “The Complementing Condition in Elasticity.” 2014. Thesis, University of Tennessee – Knoxville. Accessed March 01, 2021. https://trace.tennessee.edu/utk_gradthes/2748.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ramanan, Lavanya. “The Complementing Condition in Elasticity.” 2014. Web. 01 Mar 2021.

Vancouver:

Ramanan L. The Complementing Condition in Elasticity. [Internet] [Thesis]. University of Tennessee – Knoxville; 2014. [cited 2021 Mar 01]. Available from: https://trace.tennessee.edu/utk_gradthes/2748.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ramanan L. The Complementing Condition in Elasticity. [Thesis]. University of Tennessee – Knoxville; 2014. Available from: https://trace.tennessee.edu/utk_gradthes/2748

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

27. Afonso, Suzete Maria Silva. Equações diferenciais funcionais com retardamento e impulsos em tempo variável via equações diferenciais ordinárias generalizadas.

Degree: PhD, Matemática, 2011, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-29032011-142311/ ;

►

O objetivo deste trabalho é investigar propriedades qualitativas das soluções de equações diferenciais funcionais com retardamento e impulsos em tempo variável (EDFRs impulsivas) através da… (more)

Subjects/Keywords: Delay; Equações diferenciais funcionais; Equações diferenciais ordinárias generalizadas; Functional differential equations; Generalized ordinary differential equations; Impulsos; Retardamento

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Afonso, S. M. S. (2011). Equações diferenciais funcionais com retardamento e impulsos em tempo variável via equações diferenciais ordinárias generalizadas. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/55/55135/tde-29032011-142311/ ;

Chicago Manual of Style (16^th Edition):

Afonso, Suzete Maria Silva. “Equações diferenciais funcionais com retardamento e impulsos em tempo variável via equações diferenciais ordinárias generalizadas.” 2011. Doctoral Dissertation, University of São Paulo. Accessed March 01, 2021. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-29032011-142311/ ;.

MLA Handbook (7^th Edition):

Afonso, Suzete Maria Silva. “Equações diferenciais funcionais com retardamento e impulsos em tempo variável via equações diferenciais ordinárias generalizadas.” 2011. Web. 01 Mar 2021.

Vancouver:

Afonso SMS. Equações diferenciais funcionais com retardamento e impulsos em tempo variável via equações diferenciais ordinárias generalizadas. [Internet] [Doctoral dissertation]. University of São Paulo; 2011. [cited 2021 Mar 01]. Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-29032011-142311/ ;.

Council of Science Editors:

Afonso SMS. Equações diferenciais funcionais com retardamento e impulsos em tempo variável via equações diferenciais ordinárias generalizadas. [Doctoral Dissertation]. University of São Paulo; 2011. Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-29032011-142311/ ;

Universidade Estadual de Campinas

28. Delboni, Roberta Regina, 1979-. Estudo de estratégia de contenção do crescimento de micro-organismos patogênicos em alimentos: Evaluating strategies for the containment of pathogenic microorganisms development in processed foods.

Degree: 2015, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307200

► Abstract: Microbial contamination is a big problem for the food industry and also for the public health. The economic losses occur due to civil process… (more)

Subjects/Keywords: Bacteriocinas; Equações diferenciais ordinárias; Equações diferenciais parciais não-lineares; Ondas viajantes; Bacteriocins; Ordinary differential equations; Nonlinear partial differential equations; Traveling waves

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APA (6^th Edition):

Delboni, Roberta Regina, 1. (2015). Estudo de estratégia de contenção do crescimento de micro-organismos patogênicos em alimentos: Evaluating strategies for the containment of pathogenic microorganisms development in processed foods. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/307200

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Delboni, Roberta Regina, 1979-. “Estudo de estratégia de contenção do crescimento de micro-organismos patogênicos em alimentos: Evaluating strategies for the containment of pathogenic microorganisms development in processed foods.” 2015. Thesis, Universidade Estadual de Campinas. Accessed March 01, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307200.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Delboni, Roberta Regina, 1979-. “Estudo de estratégia de contenção do crescimento de micro-organismos patogênicos em alimentos: Evaluating strategies for the containment of pathogenic microorganisms development in processed foods.” 2015. Web. 01 Mar 2021.

Vancouver:

Delboni, Roberta Regina 1. Estudo de estratégia de contenção do crescimento de micro-organismos patogênicos em alimentos: Evaluating strategies for the containment of pathogenic microorganisms development in processed foods. [Internet] [Thesis]. Universidade Estadual de Campinas; 2015. [cited 2021 Mar 01]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307200.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Delboni, Roberta Regina 1. Estudo de estratégia de contenção do crescimento de micro-organismos patogênicos em alimentos: Evaluating strategies for the containment of pathogenic microorganisms development in processed foods. [Thesis]. Universidade Estadual de Campinas; 2015. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307200

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Saskatchewan

29. Marsh, Megan. An assessment of numerical methods for cardiac simulation.

Degree: 2012, University of Saskatchewan

URL: http://hdl.handle.net/10388/ETD-2012-01-295

► Solving the mathematical models of the electrical activity in the heart is difficult mainly due to the complexity of the models required to capture the… (more)

▼ Solving the mathematical models of the electrical activity in the heart is difficult mainly due to the complexity of the models required to capture the electrochemical details of the organ. A variety of mathematical models has been developed to describe the electrical activity of individual heart cells. Cardiac cells respond to an electrical stimulus, causing ions to flow across the cell membrane, changing the electrical potential difference between the interior and the exterior of the cell. Cardiac cell models describe the potential difference across the cell membrane, and depending on the complexity of the model, the ion concentrations and the movement of ions through the cell membrane. This thesis studies 37 cardiac cell models and compares the efficiency of the Forward Euler and Rush-Larsen methods, as well as two generalized Rush-Larsen methods (of order one and order two). The Backward Euler method is compared for six of the 37 models and type-insensitive methods are compared for four of the 37 models. From the results, it is determined that the Rush-Larsen method is the most efficient for moderately stiff models and that the generalized Rush-Larsen methods perform well on the stiff models. The type-insensitive methods are more efficient than the single methods for each of the four models considered. The bidomain model combines a cardiac cell model with two partial differential equations that model the propagation of the electrical activity throughout the entire heart. Simulations of the bidomain model are computationally expensive, necessitating improvements to the numerical methods used to solve the model. In order to determine whether the cell model results can be applied to the bidomain model, a one-dimensional simulation of the bidomain model is considered and solved using the Chaste software package developed by the Computational Biology Group at Oxford University Computing Laboratory, together with additions written for this thesis. The cellular electrical activity within the bidomain model is modelled by eight of the 37 cell models previously studied, chosen to represent a range of the available models. From these results, it is shown that the cell model results are directly applicable to the one-dimensional bidomain problem. The first-order generalized Rush-Larsen method drastically reduces computation time for the two stiffest models, and the Rush-Larsen method performs optimally for the moderately stiff models. One of the de facto standards, the Forward Euler method, is shown to perform poorly for seven of the eight one-dimensional bidomain simulations. Advisors/Committee Members: Spiteri, Raymond J., Patrick, George W., Soteros, Chris.

Subjects/Keywords: Heart simulation; efficient numerical methods; stiffness; ordinary differential equations; bidomain model; partial differential equations; simulation of electrophysiological models

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APA (6^th Edition):

Marsh, M. (2012). An assessment of numerical methods for cardiac simulation. (Thesis). University of Saskatchewan. Retrieved from http://hdl.handle.net/10388/ETD-2012-01-295

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Marsh, Megan. “An assessment of numerical methods for cardiac simulation.” 2012. Thesis, University of Saskatchewan. Accessed March 01, 2021. http://hdl.handle.net/10388/ETD-2012-01-295.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Marsh, Megan. “An assessment of numerical methods for cardiac simulation.” 2012. Web. 01 Mar 2021.

Vancouver:

Marsh M. An assessment of numerical methods for cardiac simulation. [Internet] [Thesis]. University of Saskatchewan; 2012. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/10388/ETD-2012-01-295.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Marsh M. An assessment of numerical methods for cardiac simulation. [Thesis]. University of Saskatchewan; 2012. Available from: http://hdl.handle.net/10388/ETD-2012-01-295

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Southern Mississippi

30. Ocloo, Cyril. A Time Integration Method of Approximate Particular Solutions for Nonlinear Ordinary Differential Equations.

Degree: MS, 2020, University of Southern Mississippi

URL: https://aquila.usm.edu/masters_theses/729

► We consider a time-dependent method which is coupled with the method of approximate particular solutions (MAPS) of Delta-shaped basis functions and the method of… (more)

Subjects/Keywords: Time; integration; method; Numerical Analysis and Computation; Ordinary Differential Equations and Applied Dynamics; Other Applied Mathematics; Partial Differential Equations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ocloo, C. (2020). A Time Integration Method of Approximate Particular Solutions for Nonlinear Ordinary Differential Equations. (Masters Thesis). University of Southern Mississippi. Retrieved from https://aquila.usm.edu/masters_theses/729

Chicago Manual of Style (16^th Edition):

Ocloo, Cyril. “A Time Integration Method of Approximate Particular Solutions for Nonlinear Ordinary Differential Equations.” 2020. Masters Thesis, University of Southern Mississippi. Accessed March 01, 2021. https://aquila.usm.edu/masters_theses/729.

MLA Handbook (7^th Edition):

Ocloo, Cyril. “A Time Integration Method of Approximate Particular Solutions for Nonlinear Ordinary Differential Equations.” 2020. Web. 01 Mar 2021.

Vancouver:

Ocloo C. A Time Integration Method of Approximate Particular Solutions for Nonlinear Ordinary Differential Equations. [Internet] [Masters thesis]. University of Southern Mississippi; 2020. [cited 2021 Mar 01]. Available from: https://aquila.usm.edu/masters_theses/729.

Council of Science Editors:

Ocloo C. A Time Integration Method of Approximate Particular Solutions for Nonlinear Ordinary Differential Equations. [Masters Thesis]. University of Southern Mississippi; 2020. Available from: https://aquila.usm.edu/masters_theses/729

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Open Access Theses and Dissertations