A Galerkin method for singular two point linear boundary value problems

In this paper we use variational techniques to address the problem of existence and uniqueness of solutions of a class of singular two-point boundary value problems. We then use a Galerkin method with special basis functions to discretize the problem. We prove convergence of the solution of the discrete problem to that of continuous problem and give the order of convergence in various energy and uniform norms. The orders of convergence obtained are optimal.