RESEARCH ARTICLE An Algorithm for Solving Second Order Nonlinear Singular Perturbation Boundary Value Problems

with a boundary layer at one end point. Using singular perturbation analysis the original problem is replaced by an asymptotically equivalent first-order initial-value problem (IVP). Then, a variable step size initial-value algorithm is applied to solve this IVP in the boundary layer region. The algorithm is derived based on the piecewise linearization of the obtained IVP and its analytical integration over a non-uniform mesh. The step size is determined directly according to the variation of the solution within a step in the boundary layer region and results in two-term recurrence relation with controlled step size. Some numerical examples are given to illustrate the validity of the given method. It is observed that the present method approximates the exact solution very well