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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

   

 

The FD-method for solving Sturm-Liouville problems with special singular differential operator


Authors: V. L. Makarov, D. V. Dragunov and Ya. V. Klimenko
Journal: Math. Comp. 82 (2013), 953-973
MSC (2010): Primary 65L15, 65L20; Secondary 33D15, 68W99
Published electronically: August 8, 2012
MathSciNet review: 3008844
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Abstract: A superexponentially convergent method for solving the Sturm-Liouville problem with Legendre's differential operator is given. The presented method (called the FD-method) is based on the coefficient approximation methods (CAM) and the homotopy approach. Sufficient convergence conditions of the proposed method are stated and rigorously substantiated. The algorithms for software implementation of the proposed method are described. The numerical examples included in the paper confirm the theoretical conclusions.


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Additional Information

V. L. Makarov
Affiliation: Department of Numerical Mathematics, Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs’ka Str., Kyiv-4, 01601, Ukraine
Email: makarov@imath.kiev.ua

D. V. Dragunov
Affiliation: Department of Numerical Mathematics, Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs’ka Str., Kyiv-4, 01601, Ukraine
Email: dragunovdenis@gmail.com

Ya. V. Klimenko
Affiliation: Department of Numerical Mathematics, Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs’ka Str., Kyiv-4, 01601, Ukraine
Email: oldyara@gmail.com

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02634-2
Keywords: Singular Sturm-Liouville problem, FD-method, coefficient approximation methods, Legendre functions, Stenger’s formula
Received by editor(s): August 1, 2011
Received by editor(s) in revised form: October 6, 2011
Published electronically: August 8, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.