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An efficient technique for finding the eigenvalues and the eigenelements of fourth-order Sturm-Liouville problems

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Abstract

In this paper an efficient method based on Legendre-Galerkin method for computing the eigenvalues of fourth-order Sturm-Liouville problem subject to a kind of fixed boundary conditions is developed. Properties of Legendre polynomials are first presented, these properties are then utilized to reduce the eigenvalues of fourth-order Sturm-Liouville problem to some linear algebraic equations. The method is computationally attractive, and applications are demonstrated through an illustrative example and a comparisons with other methods are made.

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Acknowledgments

The authors are grateful for the referees for their valuable comments and suggestions on the original manuscript.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Engineering, Mansoura University, Mansoura, Egypt

    Mohamed El-Gamel & M. S. El-Azab

  2. Basic and Applied Science Department, College of Engineering and Technology, Arab Academy for Science, Technology, and Maritime Transport, Cairo, Egypt

    Mohamed Fathy

Authors
  1. Mohamed El-Gamel
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  2. M. S. El-Azab
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  3. Mohamed Fathy
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Correspondence to Mohamed El-Gamel.

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El-Gamel, M., El-Azab, M.S. & Fathy, M. An efficient technique for finding the eigenvalues and the eigenelements of fourth-order Sturm-Liouville problems. SeMA 74, 37–56 (2017). https://doi.org/10.1007/s40324-016-0079-8

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  • DOI: https://doi.org/10.1007/s40324-016-0079-8

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