A fully discrete θ-method for solving semi-linear reaction-diffusion equations with time-variable delay

摘要

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(τ~2 +h~2 ) (resp. O(τ+h~2 )) when θ = 1/2 (resp. θ ≠ 1/2), 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.