Special Second Order Non Symmetric Fitted Method for Singular Perturbation Problems

Abstract

In this paper, we present a special second order non symmetric fitted difference method for solving singular perturbed two point boundary value problems having boundary layer at one end. We introduce a fitting factor in the special second order non symmetric finite difference scheme which takes care of the rapid changes occur that in the boundary layer. The value of this fitting factor is obtained from the theory of singular perturbations. The discrete invariant imbedding algorithm is used to solve the tridiagonal system obtained by the method. We discuss the existence and uniqueness of the discrete problem along with stability estimates and the convergence of the method. We present the maximum absolute errors in numerical results to illustrate the proposed method.

Keywords: Singularly perturbed two-point boundary value problem, Boundary layer, Fitting factor, Maximum absolute error