Cubic spline solution of nonlinear singularly perturbed boundary value problems via initial value method

In this paper, a cubic spline solution of nonlinear singularly perturbed two-point boundary value problems exhibiting boundary layers is presented via initial value method. The method is distinguished by the following fact: The original problem is approximated asymptomatically by two first order unperturbed initial value problems which are, in turn, solved using polynomial cubic spline approximation method. Error estimate and numerical results are presented to assess the accuracy and the performance of the method. It is observed that the present method approximates the exact solution very well overall the problem entire domain.