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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.

Journal Article Type Article
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
APA6 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
Publisher URL http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=zvmmf&paperid=1564&option_lang=eng