A Difference Scheme Using Spline for a Class of Singular Boundary Value Problem

Abstract

In this paper, a finite difference scheme using cubic splines has been discussed to find the numerical solution for a class of singular two point boundary value problems for certain ordinary differential equations. The cubic spline approximation leads to the tridiagonal system of equations, which can be solved using Newton’s method. Second order convergence of the method has been established for quite general conditions. Two numerical examples are given to demonstrate the method and verify the second order accuracy.