Spline Finite Difference Methods and Their Extrapolation for Singular Two-Point Boundary Value Problems

Abstract

In this paper we consider a class of singular two-point boundary value problem: $(x^αu')'=f(x,u),u(0)=A,u(1)=B,0＜α＜1$. The asymptotic expression of the spline finite difference solution for the problem is obtained. By using the asymptotic expression, Richardson's extrapolation can be done and the accuracy of numerical solution can be improved. Some numerical examples are given in illustration of this theory.