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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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