Computation of Eigenvalues of the Fourth Order Sturm-Liouville BVP by Galerkin Weighted Residual Method

The aim of this paper is to compute eigenvalues of fourth order regular Sturm-Liouville Boundary Value Problems (SLP). We propose the Galerkin weighted residual method with Bernstein polynomials as basis functions to approximate the solutions of SLP. We derive rigorous matrix formulations to compute the eigenvalues of the SLP. Special care has been given about how the polynomials satisfy the corresponding homogeneous form of Dirichlet boundary conditions. The approximate eigenvalues are compared with the exact result and also compared with the relevant studies by some authors. The results in this study agree with that of the other relevant articles.