Year: 1999
Author: Hai-Jun Wu, Rong-Hua Li
Journal of Computational Mathematics, Vol. 17 (1999), Iss. 4 : pp. 397–418
Abstract
The object of this paper is to establish the relation between stability and convergence of the numerical methods for the evolution equation $u_t-Au-f(u)=g(t)$ on Banach space $V$, and to prove the long-time error estimates for the approximation solutions. At first, we give the definition of long-time stability, and then prove the fact that stability and compatibility imply the uniform convergence on the infinite time region. Thus, we establish a general frame in order to prove the long-time convergence. This frame includes finite element methods and finite difference methods of the evolution equations, especially the semilinear parabolic and hyperbolic partial differential equations. As applications of these results we prove the estimates obtained by Larsson [5] and Sanz-serna and Stuart [6].
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1999-JCM-9111
Journal of Computational Mathematics, Vol. 17 (1999), Iss. 4 : pp. 397–418
Published online: 1999-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Stability Compatibility Convergence Reaction-diffusion equation Long-time error estimates.