Long Time Asymptotic Behavior of Solution of Difference Scheme for a Semilinear Parabolic Equation (Journal of Computational Mathematics, 1998)
In this paper we prove that the solution of implicit difference scheme for a semilinear parabolic equation converges to the solution of difference scheme for the corresponding nonlinear stationary problem as $t→∞$. For the discrete solution of nonlinear parabolic problem, we get its long time asymptotic behavior which is similar to that of the continuous solution. For simplicity, we consider one-dimensional problem.
Keywords: Asymptotic behavior; implicit difference scheme; semilinear parabolic equation.