Year: 2015
Author: V. Thomée, A.S. Vasudeva Murthy
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 1 : pp. 17–32
Abstract
We consider the numerical solution by finite difference methods of the heat equation in one space dimension, with a nonlocal integral boundary condition, resulting from the truncation to a finite interval of the problem on a semi-infinite interval. We first analyze the forward Euler method, and then the $θ$-method for $0 < θ ≤ 1$, in both cases in maximum-norm, showing $O(h^2 + k)$ error bounds, where $h$ is the mesh-width and $k$ the time step. We then give an alternative analysis for the case $θ = 1/2$, the Crank-Nicolson method, using energy arguments, yielding a $O(h^2$ + $k^{3/2}$) error bound. Special attention is given the approximation of the boundary integral operator. Our results are illustrated by numerical examples.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1406-m4443
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 1 : pp. 17–32
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Heat equation Artificial boundary conditions unbounded domains product quadrature.
Author Details
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