A note on compact finite difference method for reaction-diffusion equations with delay

摘要

In this short study, we investigate the long time stability of the compact finite difference method for the reaction-diffusion equations with delay. It is shown that the spatial discretization leads to a reduction of the asymptotic stability region of the corresponding PDE if the compact finite difference method is applied to discretize the diffusion operator. A way to improve the stability region of the method is also presented. Finally, some numerical experiments are proposed to confirm our findings.