UNIFORMLY CONVERGENT NUMERICAL SCHEME FOR SINGULARLY PERTURBED PARABOLIC DELAY DIFFERENTIAL EQUATIONS

In this paper, numerical treatment of singularly perturbed parabolic delay differential equations is considered. The considered problem have small delay on the spatial variable of the reaction term. To treat the delay term, Taylor series approximation is applied. The resulting singularly perturbed parabolic PDEs is solved using Crank Nicolson method in temporal direction with non-standard finite difference method in spatial direction. A detail stability and convergence analysis of the scheme is given. We proved the uniform convergence of the scheme with order of convergence O(N- 1 + (Delta t)(2)), where N is the number of mesh points in spatial discretization and Delta t is mesh length in temporal discretization. Two test examples are used to validate the theoretical results of the scheme.