Long Time Asymptotic Behavior of Solution of Difference Scheme for a Semilinear Parabolic Equation (II)

Abstract

In this paper we prove the solution of explicit difference scheme for a semilinear parabolic equation converges to the solution of difference scheme for the relevant nonlinear stationary problem as $t \rightarrow \infty$. For nonlinear parabolic problem, we obtain the long time asymptotic behavior of its discrete solution which is analogous to that of its continuous solution. For simplicity, we discuss one-dimensional problem.