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You searched for +publisher:"University of North Carolina" +contributor:("Jia, Jun"). One record found.

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University of North Carolina

1. Jia, Jun. Krylov deferred correction methods for differential equations with algebraic constraints.

Degree: Mathematics, 2006, University of North Carolina

In this dissertation, we introduce a new class of spectral time stepping methods for efficient and accurate solutions of ordinary differential equations (ODEs), differential algebraic equations (DAEs), and partial differential equations (PDEs). The methods are based on applying spectral deferred correction techniques as preconditioners to Picard integral collocation formulations, least squares based orthogonal polynomial approximations are computed using Gaussian type quadratures, and spectral integration is used instead of numerically unstable differentiation. For ODE problems, the resulting Krylov deferred correction (KDC) methods solve the preconditioned nonlinear system using Newton-Krylov schemes such as Newton-GMRES method. For PDE systems, method of lines transpose (MoLT ) couples the KDC techniques with fast elliptic equation solvers based on integral equation formulations and fast algorithms. Preliminary numerical results show that the new methods are of arbitrary order of accuracy, extremely stable, and very competitive with existing techniques, particularly when high precision is desired. Advisors/Committee Members: Jia, Jun, Huang, Jingfang.

Subjects/Keywords: College of Arts and Sciences; Department of Mathematics

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

APA (6th Edition):

Jia, J. (2006). Krylov deferred correction methods for differential equations with algebraic constraints. (Thesis). University of North Carolina. Retrieved from https://cdr.lib.unc.edu/record/uuid:9d01cdbe-faad-4300-b91c-8bbfe079d3cd

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

Chicago Manual of Style (16th Edition):

Jia, Jun. “Krylov deferred correction methods for differential equations with algebraic constraints.” 2006. Thesis, University of North Carolina. Accessed November 29, 2020. https://cdr.lib.unc.edu/record/uuid:9d01cdbe-faad-4300-b91c-8bbfe079d3cd.

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

MLA Handbook (7th Edition):

Jia, Jun. “Krylov deferred correction methods for differential equations with algebraic constraints.” 2006. Web. 29 Nov 2020.

Vancouver:

Jia J. Krylov deferred correction methods for differential equations with algebraic constraints. [Internet] [Thesis]. University of North Carolina; 2006. [cited 2020 Nov 29]. Available from: https://cdr.lib.unc.edu/record/uuid:9d01cdbe-faad-4300-b91c-8bbfe079d3cd.

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

Council of Science Editors:

Jia J. Krylov deferred correction methods for differential equations with algebraic constraints. [Thesis]. University of North Carolina; 2006. Available from: https://cdr.lib.unc.edu/record/uuid:9d01cdbe-faad-4300-b91c-8bbfe079d3cd

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

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