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

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.