International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 5, Pages 257-269

A higher-order method for nonlinear singular two-point boundary value problems

K. M. Furati and M. A. El-Gebeily

Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 18 May 2001; Revised 3 October 2001

Copyright © 2002 K. M. Furati and M. A. El-Gebeily. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a finite difference method for a general class of nonlinear singular two-point boundary value problems. The order of convergence of the method for such a general class of problems is higher than the previous reported methods. The method yields a fourth-order convergence for the special case p(x)=w(x)=xα, α1.