Asymptotic initial value methods for two-parameter singularly perturbed boundary value problems for second order ordinary differential equations

Abstract

In this paper some numerical methods are presented for singularly perturbed two-point boundary value problems for second order ordinary differential equations with two small parameters multiplying the derivatives. These methods are distinguished by the fact that, initial value problems and/or terminal value problems are constructed/deduced from the given boundary value problem and then solved by a fitted operator method. Further error estimates are derived. The methods suggested are simple to use and easy to implement. The important aspect is that some of the methods suggested are well suited for parallel computing. Examples are provided to illustrate the methods.