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Variational Estimation Methods for Sturm–Liouville Problems

Author

Listed:
  • Elena Corina Cipu

    (Department of Applied Mathematics, University Politehnica of Bucharest, Spl. Independentei, No. 313, RO-060042 Bucharest, Romania
    CiTi, Faculty of Applied Sciences, University Politehnica of Bucharest, Spl. Independentei, No. 313, RO-060042 Bucharest, Romania)

  • Cosmin Dănuţ Barbu

    (Department of Applied Mathematics, University Politehnica of Bucharest, Spl. Independentei, No. 313, RO-060042 Bucharest, Romania)

Abstract

In this paper, we are concerned with approach solutions for Sturm–Liouville problems (SLP) using variational problem (VP) formulation of regular SLP. The minimization problem (MP) is also set forth, and the connection between the solution of each formulation is then proved. Variational estimations (the variational equation associated through the Euler–Lagrange variational principle and Nehari’s method, shooting method and bisection method) and iterative variational methods (He’s method and HPM) for regular RSL are unitary presented in final part of the paper, which ends with applications.

Suggested Citation

  • Elena Corina Cipu & Cosmin Dănuţ Barbu, 2022. "Variational Estimation Methods for Sturm–Liouville Problems," Mathematics, MDPI, vol. 10(20), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3728-:d:938794
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    References listed on IDEAS

    as
    1. Hongjie Guo & Jiangang Qi, 2020. "Sturm–Liouville Problems Involving Distribution Weights and an Application to Optimal Problems," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 842-857, March.
    2. Upeksha Perera & Christine Böckmann, 2020. "Solutions of Sturm-Liouville Problems," Mathematics, MDPI, vol. 8(11), pages 1-14, November.
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