Long Time Asymptotic Behavior of Solutions of Explicit Difference Scheme for Semilinear Parabolic Equations (Journal of Computational Mathematics, 2002)
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 $t→∞$. We get the long time asymptotic behavior of the discrete solutions which is interested in comparing to the case of continuous solutions.