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Numerical solution of parabolic equations by the box scheme


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.


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.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Keller, Herbert Bishop
Thesis Committee:
  • Unknown, Unknown
Defense Date:22 September 1972
Record Number:CaltechTHESIS:04012013-103558891
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7571
Deposited By: Dan Anguka
Deposited On:01 Apr 2013 17:49
Last Modified:09 Nov 2022 19:20

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