LONG TIME ASYMPTOTIC BEHAVIOR OF SOLUTION OF DIFFERENCE SCHEME FOR A SEMILINEAR PARABOLIC EQUATION (Ⅱ)

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→∞. 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.