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

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• 作者：Mohamed El-Gamel ; M. S. El-Azab ; Mohamed Fathy
• 关键词：Legendre ; Galerkin ; Eigenvalues ; Eigenfunctions ; Sturm ; Liouville
• 刊名：SeMA Journal
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：74
• 期：1
• 页码：37-56
• 全文大小：
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Milan
• ISSN：2281-7875
• 卷排序：74

文摘

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.