The Double Exponential Sinc Collocation Method for Singular Sturm-Liouville Problems

TL;DR

This paper introduces a highly accurate and efficient double exponential Sinc collocation method for computing eigenvalues of singular Sturm-Liouville problems, demonstrating exponential convergence and advantages over single exponential methods.

Contribution

The paper develops a novel double exponential Sinc collocation approach that improves accuracy and convergence speed for singular Sturm-Liouville eigenvalue problems.

Findings

The method produces a symmetric positive-definite eigenvalue system.

Numerical results show exponential convergence.

Compared to single exponential methods, it offers clear advantages.

Abstract

Sturm-Liouville problems are abundant in the numerical treatment of scientific and engineering problems. In the present contribution, we present an efficient and highly accurate method for computing eigenvalues of singular Sturm-Liouville boundary value problems. The proposed method uses the double exponential formula coupled with Sinc collocation method. This method produces a symmetric positive-definite generalized eigenvalue system and has exponential convergence rate. Numerical examples are presented and comparisons with single exponential Sinc collocation method clearly illustrate the advantage of using the double exponential formula.