@Article{JCM-17-4,
author = {Wu, Hai-Jun and Rong-Hua, Li},
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 = {<p style="text-align: justify;">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.&nbsp;As applications of these results we prove
the estimates obtained by Larsson [5] and Sanz-serna and Stuart [6].</p>},
issn = {1991-7139},
doi = {https://doi.org/1999-JCM-9111},
url = {https://global-sci.com/article/85636/the-stability-and-convergence-of-computing-long-time-behaviour}
}