Computing the eigenvalues of fourth order Sturm-Liouville problems with Lie Group method
7(1) : 1-12
Article Type: Original Article
Abstract: 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.