Fitted-Stable Finite Difference Method for Singularly Perturbed Two Point Boundary Value Problems

Abstract

A fitted-stable central difference method is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right) of the interval. A fitting factor is introduced in second order stable central difference scheme (SCD Method) and its value is obtained using the theory of singular perturbations. Thomas Algorithm (also known as Discrete Invariant Imbedding Algorithm) is used to solve the resulting tri-diagonal system. To validate the applicability of the method, some linear and non-linear examples have been solved for different values of the perturbation parameter. The numerical results are tabulated and compared with exact solutions. The error bound and convergence of the proposed method has also been established. From the results, it is observed that the present method approximates the exact solution very well.

Key words: Singular perturbation problems, stable, central differences, fitted methods