Volume 17, Issue 4
The Stability and Convergence of Computing Long-Time Behaviour

Hai Jun Wu & Rong Hua Li

DOI:

J. Comp. Math., 17 (1999), pp. 397-418

Published online: 1999-08

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  • 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 them 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.

  • Keywords

Compatibility Covergence Reaction-diffusion equation Longtime error estimates

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@Article{JCM-17-397, author = {}, title = {The Stability and Convergence of Computing Long-Time Behaviour}, journal = {Journal of Computational Mathematics}, year = {1999}, volume = {17}, number = {4}, pages = {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 them 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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9111.html} }
TY - JOUR T1 - The Stability and Convergence of Computing Long-Time Behaviour JO - Journal of Computational Mathematics VL - 4 SP - 397 EP - 418 PY - 1999 DA - 1999/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9111.html KW - Compatibility KW - Covergence KW - Reaction-diffusion equation KW - Longtime error estimates AB - 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 them 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.
Hai Jun Wu & Rong Hua Li. (1970). The Stability and Convergence of Computing Long-Time Behaviour. Journal of Computational Mathematics. 17 (4). 397-418. doi:
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