Computing the eigenvalues of fourth order Sturm-Liouville problems with Lie Group method

Iranian Journal of Numerical Analysis and Optimization

مقاله 2، دوره 7، شماره 1 - شماره پیاپی 11، تیر 2017، صفحه 1-12   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v7i1.44788

نویسنده

H. Mirzaei^*

Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.

چکیده

‎In this paper, we formulate the fourth order Sturm-Liouville problem (FSLP) as a Lie group matrix differential equation. By solving this ma- trix differential equation by Lie group Magnus expansion, we compute the eigenvalues of the FSLP. The Magnus expansion is an infinite series of multiple integrals of Lie brackets. The approximation is, in fact, the truncation of Magnus expansion and a Gaussian quadrature are used to evaluate the integrals. Finally, some numerical examples are given.

کلیدواژه‌ها

Lie group method؛ Fourth order Sturm-Liouville problem؛ Mag- nus expansion

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