Convergence Analysis of Spline Solution of Certain Two-Point Boundary Value Problems

Abstract

The smooth approximate solution of second order boundary value problems are developed by using non-polynomial quintic spline function. We obtained the classes of numerical methods, which are second, fourth and six-order. For a speci c choice of the parameters involved in a non-polynomial spline, truncation errors are given. A new approach convergence analysis of the presented methods are discussed. Three test examples are considered in our references. By considering the maximum absolute errors in the solution at grid points and tabulated in tables for di erent choices of step size, we conclude that our presented methods produce accurate results in comparison with those obtained by existing methods.