Long Time Asymptotic Behavior of Solutions of Explicit Difference Scheme for Semilinear Parabolic Equations

Abstract

In this paper we prove that the solution of explicit difference scheme for a class of semilinear parabolic equations converges to the solution of difference schemes for the corresponding nonlinear elliptic equations in $H^1$ norm as $t\rightarrow\infty$. We get the long time asymptotic behavior of the discrete solutions which is interested in comparing to the case of continuous solutions.