The Sturm-Liouville eigenvalue problem - a numerical solution using the Control Volume Method

Abstract

Abstract. The solution of the 1D Sturm-Liouville problem using the Control Volume Method is discussed. The second order linear differential equation with homogeneous boundary conditions is discretized and converted to the system of linear algebraic equations. The matrix associated with this system is tridiagonal and eigenvalues of this system are an approximation of the real eigenvalues of the boundary value problem. The numerical results of the eigenvalues for various cases and the experimental rate of convergence are presented.

Exact and numerical solutions of the fractional Sturm–Liouville problem

“…the Pruess, shooting and finite difference methods [4,26]. In paper [29], the control volume method is used to determine the eigenvalues of the classical Sturm-Liouville problem. However, for FSLPs involving both the left and the right derivative, the adequate set of numerical tools still requires further and extensive work.…”