Computational technique for singular boundary value problems by using Numerical Quadrature

Abstract

In problems of physics and engineering we often come across singular boundary value problems that 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 nonlinear depending upon the nature of the boundary value problem. In this paper a difference method based on nonuniform mesh for a class of singular two-point boundary value problems of the form $$\begin{gathered} (x^\alpha y')' = f(x,y), 0 < x \leqslant 1, 0 < \alpha < 1, \hfill \\ y(0) = A, y(1) = B \hfill \\ \end{gathered} $$ has been derived using Numerical Quadrature. It is shown to be order-h2 convergent for all α ∈ (0, 1). The method is illustrated computationally by two numerical examples.