Solutions of Sturm-Liouville Problems

Upeksha Perera and Christine Böckmann
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Upeksha Perera: Department of Mathematics, University of Kelaniya, Kelaniya 11600, Sri Lanka
Christine Böckmann: Institut für Mathematik, Universität Potsdam, 14476 Potsdam, Germany

Mathematics, 2020, vol. 8, issue 11, 1-14

Abstract: This paper further improves the Lie group method with Magnus expansion proposed in a previous paper by the authors, to solve some types of direct singular Sturm–Liouville problems. Next, a concrete implementation to the inverse Sturm–Liouville problem algorithm proposed by Barcilon (1974) is provided. Furthermore, computational feasibility and applicability of this algorithm to solve inverse Sturm–Liouville problems of higher order (for n = 2 , 4 ) are verified successfully. It is observed that the method is successful even in the presence of significant noise, provided that the assumptions of the algorithm are satisfied. In conclusion, this work provides a method that can be adapted successfully for solving a direct (regular/singular) or inverse Sturm–Liouville problem (SLP) of an arbitrary order with arbitrary boundary conditions.

Keywords: Sturm–Liouville problems of higher order; singular Sturm–Liouville problems; inverse Sturm–Liouville problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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