Abstract: A finite difference scheme with the accuracy of fourth order in space and second order in time is proposed for solving a nonlinear reaction-diffusion equation with time delay. Existence and uniqueness of the solution is given by the method of upper and lower solutions. A monotone iteration is also developed for the computation of the finite difference solution. The convergence of the scheme is discussed. The numerical results shows the advantages of the method.

Key words: finite difference scheme, time Delay, monotone iteration, nonlinear reaction-diffusion equation, finite difference scheme, time Delay, monotone iteration