• LINEAR TRIANGULAR ELEMENT APPROXIMATION IN THREE-PARAMETER STURM–LIOUVILLE PROBLEM

Abstract

The purpose of this paper is to use linear triangular element approximation, which is one of the forms of finite element method, to find the eigenvalues of a three-parameter linear Sturm-Liouville problem with homogeneous boundary conditions. We first reduce the original three-parameter problem into an equivalent system of one-parameter problem. We apply linear triangular element approximation on reduced form of the given problem to find the rough estimates of the eigenvalues. Using the rough estimates as starting approximation in the corresponding shooting method, we obtained the actual values of the eigenvalues. A numerical example is given to illustrate the effectiveness of the method.