A fully discrete [formula omitted]-method for solving semi-linear reaction–diffusion equations with time-variable delay

Abstract

In this paper, a fully discrete θ-method with 0≤θ≤1 is suggested to solve the initial–boundary value problem of semi-linear reaction–diffusion equations with time-variable delay. Under some appropriate conditions, a novel global stability criterion of the method is derived and it is shown that this method has the computational accuracy O(τ2+h2)(resp.O(τ+h2)) when θ=12(resp.θ≠12), where h and τ denote spatial and temporal stepsizes, respectively. Moreover, with some numerical experiments, the theoretical accuracy and global stability of the method are further illustrated.