A Meshless Method for Nonlinear, Singular and Generalized Sturm-Liouville Problems

A new numerical technique for solving generalized Sturm--Liouville problem d2w/dx2 + q(x, λ )w = 0, bl[ λ ,w(a)] = br[ λ ,w(b)] = 0 is presented. In is presented. In particular, we consider the problems when the coefficient q(x, λ) or the boundary conditions depend on the spectral parameter λ in an...

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Bibliographic Details
Published in:Computer modeling in engineering & sciences 2008, Vol.34 (3), p.227-252
Main Author: Reutskiy, S Yu
Format: Article
Language:English
Subjects:
Boundary conditions
Eigenvalues
Finite element method
Meshless methods
Schrodinger equation
Online Access:Get full text
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Summary:A new numerical technique for solving generalized Sturm--Liouville problem d2w/dx2 + q(x, λ )w = 0, bl[ λ ,w(a)] = br[ λ ,w(b)] = 0 is presented. In is presented. In particular, we consider the problems when the coefficient q(x, λ) or the boundary conditions depend on the spectral parameter λ in an arbitrary nonlinear manner. The method presented is based on mathematically modelling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the eigenvalues. The same technique can be applied to a very wide class of the eigenproblems: the Sturm--Liouville problems, the Schrodinger equation, the non-classical non-linear Sturm--Liouville problems, periodic problems. The results of the numerical experiments justifying the method are presented.
ISSN:1526-1492
1526-1506
DOI:10.3970/cmes.2008.034.227