Citation
Fong, Kirby William (1973) Numerical Solution of Parabolic Equations by the Box Scheme. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/SV2E-JZ49. https://resolver.caltech.edu/CaltechTHESIS:04012013-103558891
Abstract
The box scheme proposed by H. B. Keller is a numerical method for solving parabolic partial differential equations. We give a convergence proof of this scheme for the heat equation, for a linear parabolic system, and for a class of nonlinear parabolic equations. Von Neumann stability is shown to hold for the box scheme combined with the method of fractional steps to solve the two-dimensional heat equation. Computations were performed on Burgers' equation with three different initial conditions, and Richardson extrapolation is shown to be effective.
| Item Type: | Thesis (Dissertation (Ph.D.)) |
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| Subject Keywords: | (Applied Mathematics) |
| Degree Grantor: | California Institute of Technology |
| Division: | Physics, Mathematics and Astronomy |
| Major Option: | Applied Mathematics |
| Thesis Availability: | Public (worldwide access) |
| Research Advisor(s): |
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| Thesis Committee: |
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| Defense Date: | 22 September 1972 |
| Record Number: | CaltechTHESIS:04012013-103558891 |
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:04012013-103558891 |
| DOI: | 10.7907/SV2E-JZ49 |
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 7571 |
| Collection: | CaltechTHESIS |
| Deposited By: | Dan Anguka |
| Deposited On: | 01 Apr 2013 17:49 |
| Last Modified: | 16 Jul 2024 21:21 |
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