THE STABILITY AND CONVERGENCE OF COMPUTINGLONG-TIME BEHAVIOUR  

作　　者：HaI-jun Wu Rong-hua Li(Institute of Mathematics, Jilin University, Changchun 130023, China) 

出　　处：《Journal of Computational Mathematics》1999年第4期397-418,共22页计算数学（英文）

摘　　要：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].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].

关 键 词：STABILITY compatibility covergence reaction-diffusion equation long-time error estimates 

分 类 号：O175[理学—数学]