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An efficient method to approximate eigenfunctions and high-index eigenvalues of regular Sturm–Liouville problems

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  • Dehghan, M.

Abstract

The computation of the eigenvalues of a Sturm–Liouville problem is a difficult task, when high-index eigenvalues are computed. In most previous methods, it can be seen that the uncertainty of the results increases as the estimated eigenvalues grow larger. This paper is to present some new methods in which, not only the error of calculating the higher eigenvalues does not grow, but it also vanishes as eigenvalues tend to infinity. Moreover, the proposed method gives good estimates of eigenfunctions corresponding to high eigenvalues.

Suggested Citation

  • Dehghan, M., 2016. "An efficient method to approximate eigenfunctions and high-index eigenvalues of regular Sturm–Liouville problems," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 249-257.
    • Handle: RePEc:eee:apmaco:v:279:y:2016:i:c:p:249-257
    DOI: 10.1016/j.amc.2016.01.026
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    Cited by:

    1. Liu, Chein-Shan & Chen, Yung-Wei & Chang, Chih-Wen, 2024. "Precise eigenvalues in the solutions of generalized Sturm–Liouville problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 354-373.
    2. Liu, Chein-Shan & Li, Botong, 2023. "Solving Sturm–Liouville inverse problems by an orthogonalized enhanced boundary function method and a product formula for symmetric potential," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 640-660.

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