Liouville transformation, analytic approximation of transmutation operators and solution of spectral problems

Vladislav V. Kravchenko, Samy Morelos and Sergii M. Torba

Applied Mathematics and Computation, 2016, vol. 273, issue C, 321-336

Abstract: A method for solving spectral problems for the Sturm–Liouville equation (pv′)′−qv+λrv=0 based on the approximation of the Delsarte transmutation operators combined with the Liouville transformation is presented. The problem of numerical approximation of solutions and of eigendata is reduced to approximation of a pair of functions depending on the coefficients p, q and r by a finite linear combination of certain specially constructed functions related to generalized wave polynomials introduced by Khmelnytskaya et al. (2013) and Kravchenko and Torba (2015). The method allows one to compute both lower and higher eigendata with an extreme accuracy. Several necessary results concerning the action of the Liouville transformation on formal powers arising in the method of spectral parameter power series are obtained as well as the transmutation operator for the Sturm–Liouville operator 1r(ddxpddx−q).

Keywords: Sturm-liouville problem; Liouville transformation; Transmutation operator; Spectral parameter power series; Generalized wave polynomials; Analytic approximation (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:273:y:2016:i:c:p:321-336

DOI: 10.1016/j.amc.2015.10.011

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