Higher order method for singular boundary-value problems by using spline function

In problems of physics and engineering we often come across singular boundary-value problems which cannot be solved by the usual numerical methods. Special methods for solving such problems have been developed. These methods lead to banded systems, linear and non-linear depending upon the nature of boundary-value problem. In this paper, we discuss the construction of a spline function for a class of singular two-point boundary-value problems.x-α(xαu′)′=f(x,u),0