A New Method for Solving Singularly Perturbed Boundary Value Problems

In this paper, a new initial value method for solving a class of nonlinear singularly perturbed boundary value problems with a boundary layer at one end is proposed. The method is designed for the practicing engineer or applied mathematician who needs a practical tool for these problems (easy to use, modest problem preparation and ready computer implementation). Using singular perturbation analysis the method is distinguished by the following fact: the original problem is replaced by a pair of first order initial value problems; namely, a reduced problem and a boundary layer correction problem. These initial value problems are solved using classical fourth order Runge-Kutta method. Numerical examples are given to illustrate the method. It is observed that the present method approximates the exact solution very well.