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Article

Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion

by
Upeksha Perera
1,*,† and
Christine Böckmann
2
1
Department of Mathematics, University of Kelaniya, Kelaniya 11600, Sri Lanka
2
Institut für Mathematik, Universität Potsdam, 14476 Potsdam, Germany
*
Author to whom correspondence should be addressed.
†
Current address: Institut für Mathematik, Universität Potsdam, 14476 Potsdam, Germany.
Mathematics 2019, 7(6), 544; https://doi.org/10.3390/math7060544
Submission received: 7 May 2019 / Revised: 6 June 2019 / Accepted: 12 June 2019 / Published: 14 June 2019
(This article belongs to the Special Issue Numerical Analysis: Inverse Problems – Theory and Applications)
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Abstract

In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively.
Keywords: higher-order Sturm–Liouville problems; inverse Sturm–Liouville problems; Magnus expansion higher-order Sturm–Liouville problems; inverse Sturm–Liouville problems; Magnus expansion

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MDPI and ACS Style

Perera, U.; Böckmann, C. Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion. Mathematics 2019, 7, 544. https://doi.org/10.3390/math7060544

AMA Style

Perera U, Böckmann C. Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion. Mathematics. 2019; 7(6):544. https://doi.org/10.3390/math7060544

Chicago/Turabian Style

Perera, Upeksha, and Christine Böckmann. 2019. "Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion" Mathematics 7, no. 6: 544. https://doi.org/10.3390/math7060544

APA Style

Perera, U., & Böckmann, C. (2019). Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion. Mathematics, 7(6), 544. https://doi.org/10.3390/math7060544

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