A Computational Approach of Singularly Perturbed Singular Boundary Value Problem using an Adaptive Spline

This paper develops a different approach for the numerical solution of singularly perturbed two-point singular boundary-value problems using an adaptive spline. The difference method is designed for nonstandard finite differences of the first order derivative and adaptive spline. The suggested scheme is accurate to fourth order and works for both singular and non-singular problems. Convergence analysis of a difference scheme is discussed in this paper. The numerical results are given to illustrate the efficiency of the proposed methods in comparison to the existing method in the literature.