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

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

Mathematics, 2019, vol. 7, issue 6, 1-24

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/6/544/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/6/544/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:6:p:544-:d:239941

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().