The Double Exponential Sinc Collocation Method for Singular Sturm-Liouville Problems
For researchers in numerical analysis and engineering, this method offers a more accurate and efficient approach to solving singular Sturm-Liouville problems, though it is an incremental improvement over existing Sinc collocation methods.
The paper presents a double exponential Sinc collocation method for computing eigenvalues of singular Sturm-Liouville problems, achieving exponential convergence and outperforming the single exponential variant in numerical examples.
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.