Numerical determination of the Titchmarsh-Weyl m-coefficient

Abstract

A numerical method for calculating the Titchmarsh-Weyl mα(λ)-coefficient for the differential equation d2y/dx2+ [1 - q(x)]y = 0 is tested for the cases q(x) = x and x2, for which mα(λ) has a known analytic form in terms of special functions. An independent assessment of the accuracy of our results using the analytical solution for mα(λ) and a previous numerical method enables us to demonstrate the high accuracy of our calculation.

Citation

(2000). Numerical determination of the Titchmarsh-Weyl m-coefficient. Computational Mathematics and Mathematical Physics / Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 40(1), 108-117

• Journal Article Type: Article
• Acceptance Date: May 11, 1999
• Publication Date: Dec 31, 2000
• Journal: Computational Mathematics and Mathematical Physics
• Print ISSN: 0965-5425
• Publisher: MAIK Nauka/Interperiodica
• Peer Reviewed: Peer Reviewed
• Volume: 40
• Issue: 1
• Pages: 108-117
• Public URL: https://hull-repository.worktribe.com/output/405464
• Publisher URL: http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=zvmmf&paperid=1564&option_lang=eng