Approximate computation of Sturm-Liouville problems using orthogonal polynomials

In the present thesis the historical development of Sturm-Liouville problem are given firstly. Then the method which was studied in a paper of, Ll. G. Chambers, (Chambers, 1994) and a paper of M. SEZER, (Sezer, 1996), is applied to the nonhomogenous Sturm-Liouville problem.This thesis consists of three chapters.In the first chapter the necessary preliminaries about Sturm-Liouville problem, Chebyshev polynomials, Legendre polynomials and Boubaker polynomials are given and Sturm-Liouville problem is reduced to the Liouville normal form..In the second chapter, the new method is investigated in order to obtain approximate solutions of Liouville normal form.In the final chapter, as an application, Sturm-Liouville problem is approximately solved by this method and the obtained results are compared with the reference eigenfunctions.