Application of Galerkin Weighted Residual Method to 2nd, 3rd and 4th order Sturm-Liouville Problems

The aim of this paper is to compute the eigenvalues for a class of linear Sturm-Liouville problems (SLE) with Dirichlet and mixed boundary conditions applying Galerkin Weighted Residual methods. We use Legendre polynomials over [0,1] as trial functions to approximate the solutions of second, third and fourth order SLE problems. We derive rigorous matrix formulations and special attention is given about how the polynomials satisfy the corresponding homogeneous form of Dirichlet boundary conditions of Sturm-Liouville problems. The obtained approximate eigenvalues are compared with the previous computational studies by various methods available in literature. Keywords: Sturm-Liouville problems, eigenvalue, Legendre polynomials, Galerkin method.