A fitted numerical method for a class of singularly perturbed convection delayed dominated diffusion equation

Abstract

A new exponentially fitted numerical method based on uniform mesh is proposed to obtain the solution of a class of singularly perturbed convection delayed dominated diffusion equation. The considered equation is first reduced to the ordinary singularly perturbed problem by expanding the term containing negative shift using Taylor series expansion procedure and then a three-term scheme is obtained using the theory of finite differences. A fitting factor is introduced in the derived scheme with the help of singular perturbation theory. Thomas algorithm is employed to find the solution of the resulting tridiagonal system of equations. Stability and convergence of the proposed method are discussed. The method is shown to be first accurate. Computational results for two example problems are presented for different values of the grid point, N and perturbation parameter, . It is observed that the method is capable of approximating the solution very well.