A Linearized Compact ADI Scheme for Semilinear Parabolic Problems with Distributed Delay

Abstract

Effective compact alternating direction implicit (ADI) schemes are developed for solving the semilinear parabolic problems with distributed delay. Solvability, convergence and stability of the proposed linearized schemes are studied. After that, the schemes are applied to simulate several biological models. It is shown that the obtained numerical schemes produce better convergent results than the usual ADI method, without increasing extra computational cost. The numerical results fit well the theoretical findings.