Numerical simulation of differential-difference equations with small delay in convective term and reaction term

Abstract

In this paper, we suggested a numerical scheme for solving singularly perturbed differential-difference equation with small shift. First, Taylor series used to replace the given problem as singularly perturbed boundary value problem and then subsequently a fourth order finite difference scheme is employed to solve this problem. Convergence of the method is evaluated. By considering numerical experiments, the effect of small shift on the boundary layer solution of the problem is demonstrated.