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Solutions of Sturm-Liouville Problems

Author

Listed:
  • Upeksha Perera

    (Department of Mathematics, University of Kelaniya, Kelaniya 11600, Sri Lanka
    Current address: Institut für Mathematik, Universität Potsdam, 14476 Potsdam, Germany.)

  • Christine Böckmann

    (Institut für Mathematik, Universität Potsdam, 14476 Potsdam, Germany)

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.

Suggested Citation

  • Upeksha Perera & Christine Böckmann, 2020. "Solutions of Sturm-Liouville Problems," Mathematics, MDPI, vol. 8(11), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2074-:d:448414
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    Citations

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    Cited by:

    1. Elena Corina Cipu & Cosmin Dănuţ Barbu, 2022. "Variational Estimation Methods for Sturm–Liouville Problems," Mathematics, MDPI, vol. 10(20), pages 1-18, October.
    2. Natalia P. Bondarenko, 2023. "Necessary and Sufficient Conditions for Solvability of an Inverse Problem for Higher-Order Differential Operators," Mathematics, MDPI, vol. 12(1), pages 1-27, December.
    3. Natalia P. Bondarenko, 2022. "Reconstruction of Higher-Order Differential Operators by Their Spectral Data," Mathematics, MDPI, vol. 10(20), pages 1-32, October.

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