Initial value technique for singularly perturbed two point boundary value problems using an exponentially fitted finite difference scheme

In this paper, we present an approximate method (Initial value technique) for the numerical solution of quasilinear singularly perturbed two point boundary value problems in ordinary differential equations having a boundary layer at one end (left or right) point. It is motivated by the asymptotic behavior of singular perturbation problems. The original problem is reduced to an asymptotically equivalent first order initial value problem by approximating the zeroth order term by outer solution obtained by asymptotic expansion, and then this initial value problem is solved by an exponentially fitted finite difference scheme. Some numerical examples are given to illustrate the given method. It is observed that the presented method approximates the exact solution very well for crude mesh size h.