PARAMETER UNIFORM NUMERICAL METHOD FOR SINGULARLY PERTURBED PARABOLIC DIFFERENTIAL DIFFERENCE EQUATIONS

Abstract

In this paper, a numerical study is made for solving singularly perturbed differential difference equations with small advance and delay parameters. To approximate the advance and delay terms a Taylor series expansion has been used. The resulting singularly perturbed parabolic PDE is solved by using non-standard finite difference method on uniform mesh in $ x $-direction and implicit Runge-Kutta method is used for the resulting system of IVPs in $ t $-direction. The method is shown to be accurate of order one.  A convergence analysis has been carried out to show $\varepsilon-$ uniform convergence of the proposed scheme. Two numerical examples are considered to investigate parameter uniform convergence of the proposed method.