A NOVEL TECHNIQUE FOR THE NUMERICAL APPROXIMATION OF THE SOLUTION OF SINGULARLY PERTURBED REACTION DIFFUSION EQUATION WITH DELAY AND ADVANCE

Abstract

In this paper , we undertake numerical approaches to solve singularly perturbed reaction diffusion problems ,with Dirichlet boundary conditions. To analyze the layer behaviour of such problems , we will use standard finite difference scheme with uniform mesh and fitted mesh method with a piecewise uniform mesh introduced by Ivanovich Shishkin. A numerical example of reaction-diffusion type with delay as well as advance is solved to show the effect of standard finite difference method and fitted mesh finite difference method to show the convergence between the actual solution and the solution obtained by these numerical approaches. The boundedness, stability and convergence analysis for the numerical problem are discussed. Several graphs and tables are used to show the Error and Order of Convergence of the numerical methods.