Numerical Solution of Parabolic Equations by the Box Scheme

Author: Fong, Kirby William

Year: 1973

Degree: Dissertation (Ph.D.)

Advisor: Keller, Herbert Bishop

Committee Member: Unknown, Unknown

Option: Applied Mathematics

DOI: 10.7907/SV2E-JZ49

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.

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