A Computational Method for Solving Singularly Perturbed Boundary Value Problem

Abstract

A computational method for the numerical solution of the singularly perturbed boundary value problem having a boundary layer at one end is presented in this paper. The original problem is reduced to a first order initial value problem using the asymptotic approximation. Then a fitting factor is introduced and the initial value problem is solved by using Box–Trapezoidal scheme. It is shown that the proposed technique provides first order accuracy independent of the perturbation parameter. Parameter-uniform error estimates are derived for the numerical solution. Numerical experiments are carried out to support the theoretical results.