SeMA Journal

, Volume 74, Issue 1, pp 37–56 | Cite as

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.

Keywords

Legendre Galerkin Eigenvalues Eigenfunctions Sturm-Liouville 

Mathematics Subject Classification

Primary 65L15 Secondary 34L10 
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Notes

Acknowledgments

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

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Copyright information

© Sociedad Española de Matemática Aplicada 2016

Authors and Affiliations

  • Mohamed El-Gamel
    • 1
  • M. S. El-Azab
    • 1
  • Mohamed Fathy
    • 2
  1. 1.Department of Mathematical Sciences, Faculty of EngineeringMansoura UniversityMansouraEgypt
  2. 2.Basic and Applied Science Department, College of Engineering and TechnologyArab Academy for Science, Technology, and Maritime TransportCairoEgypt

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