AN INITIAL VALUE TECHNIQUE TO SOLVE TWO-POINT NON-LINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS

The present paper builds an initial value technique for solving a two-point nonlinear singularly perturbed boundary value problem. Using the solution obtained by putting ε = 0 in the problem considered, the original problem is reduced to an equivalent system of first order initial value problems. The first order initial value problem is then solved by the non-linear single step explicit 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: Error analysis and convergence analysis of the method are also described.