Numerical solution of parabolic equations by the box scheme

Numerical solution of parabolic equations by the box scheme

<p>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 sh...

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Main Author: Fong, Kirby William
Format: Others
Published: 1973
Online Access:https://thesis.library.caltech.edu/7571/1/Fong-kw-1973.pdf
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 <https://resolver.caltech.edu/CaltechTHESIS:04012013-103558891>
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spelling ndltd-CALTECH-oai-thesis.library.caltech.edu-75712019-12-22T03:09:37Z Numerical solution of parabolic equations by the box scheme Fong, Kirby William <p>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.</p> 1973 Thesis NonPeerReviewed application/pdf https://thesis.library.caltech.edu/7571/1/Fong-kw-1973.pdf https://resolver.caltech.edu/CaltechTHESIS:04012013-103558891 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 <https://resolver.caltech.edu/CaltechTHESIS:04012013-103558891> https://thesis.library.caltech.edu/7571/
collection NDLTD
format Others
sources NDLTD
description <p>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.</p>
author Fong, Kirby William
spellingShingle Fong, Kirby William
Numerical solution of parabolic equations by the box scheme
author_facet Fong, Kirby William
author_sort Fong, Kirby William
title Numerical solution of parabolic equations by the box scheme
title_short Numerical solution of parabolic equations by the box scheme
title_full Numerical solution of parabolic equations by the box scheme
title_fullStr Numerical solution of parabolic equations by the box scheme
title_full_unstemmed Numerical solution of parabolic equations by the box scheme
title_sort numerical solution of parabolic equations by the box scheme
publishDate 1973
url https://thesis.library.caltech.edu/7571/1/Fong-kw-1973.pdf
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 <https://resolver.caltech.edu/CaltechTHESIS:04012013-103558891>
work_keys_str_mv AT fongkirbywilliam numericalsolutionofparabolicequationsbytheboxscheme
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