Numerical approximations of Sturm-Liouville eigenvalues using Chebyshev polynomial expansions method

Abstract

In this paper, an efficient technique based on the Chebyshev polynomial expansions for computing the eigenvalues of second- and fourth-order Sturm-Liouville boundary value problems is proposed. This technique reduces the given Sturm-Liouville problem to an integral equation. The resulting integral equation is then transformed into the eigenvalue equation by calculating the integrals at the grid points using the Chebyshev expansions. Thus, the required eigenvalues of the given problem are obtained by solving this eigenvalue equation. The excellent performance of this scheme is illustrated through some numerical examples, and comparison with other methods is presented.