A numerical integration method for solving singular perturbation problems

摘要

We present a numerical integration method for solving linear, singularly perturbed two point boundary value problems with a boundary layer on the left end of the underlying interval. We replace the original singular perturbation problem by an approximate first order differential equation with a small deviating argument. We use Simpson's formula for the numerical integration of the first order differential equation with a small deviating argument and then use Taylor series and finite differences to obtain a three term recurrence relationship. The proposed method is iterative on the deviating argument. Some numerical experiments have been included to demonstrate the applicability of the method.