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

A new exponentially fittednumerical method based on uniform meshis 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 perturbedproblem by expanding the term containing negative shift using Taylor series expansionprocedure and then a three-termschemeis obtained using thetheory of finite differences.Afitting factor is introduced in the derived scheme with the help of singular perturbationtheory. Thomas algorithm is employed to find the solution of the resulting tridiagonal systemof 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,Nand perturbation parameter,.It is observed that the method is capable of approximating the solution very well