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Broyden method for inverse non-symmetric Sturm-Liouville problems

  • In this paper, we propose a derivative-free method for recovering symmetric and non-symmetric potential functions of inverse Sturm-Liouville problems from the knowledge of eigenvalues. A class of boundary value methods obtained as an extension of Numerov's method is the major tool for approximating the eigenvalues in each Broyden iteration step. Numerical examples demonstrate that the method is able to reduce the number of iteration steps, in particular for non-symmetric potentials, without accuracy loss.

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Metadaten
Author:Christine Boeckmann, Athassawat Kammanee
DOI:https://doi.org/10.1007/s10543-011-0317-5
ISSN:0006-3835 (print)
Parent Title (English):BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians
Publisher:Springer
Place of publication:Dordrecht
Document Type:Article
Language:English
Year of first Publication:2011
Year of Completion:2011
Release Date:2017/03/26
Tag:Boundary value method; Broyden's method; Inverse Sturm-Liouville problem; Non-symmetric potential
Volume:51
Issue:3
Pagenumber:16
First Page:513
Last Page:528
Funder:Prince of Songkla University
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer Review:Referiert