A finite difference approximation for a class of singular boundary value problems

Abstract

Numerical solutions of singular boundary value problems have drawn considerable interest in the last two decades. This work is a contribution in that direction. The objective of this dissertation is to extend certain results in the literature to a wider class of singular self-adjoint boundary value problems with minimal constraints on the data of the problem. A finite difference method is used to approximate the solutions, eigenvalues and eigenvectors of the associated differential operators. Order h² convergence is achieved in these approximations. Numerical examples are given to demonstrate the O(h²) convergence obtained theoretically.