A Numerical Scheme for Nonlinear Singularly Perturbed Two point Boundary Value Problems using Locally Exact Integration

We consider a class of nonlinear singular perturbation problems of the form with a boundary layer at one end point. Using the theory of singular perturbations, the original problem is reduced to an asymptotically equivalent first order initial value problem. Then, a variable step size initial value algorithm is applied to solve this initial value problem in a narrow region containing the layer region. The algorithm is based on the exact integration of a locally linearized problem (on a special non uniform mesh) exhibiting uniform convergence in for any x. Some problems are solved to demonstrate the applicability and efficiency of the algorithm. It is observed that the present method approximates the exact solution very well.