@Article{cmes.2008.034.227,
AUTHOR = {S.Yu. Reutskiy},
TITLE = {A Meshless Method for Nonlinear, Singular and Generalized Sturm-Liouville Problems},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {34},
YEAR = {2008},
NUMBER = {3},
PAGES = {227--252},
URL = {http://www.techscience.com/CMES/v34n3/26715},
ISSN = {1526-1506},
ABSTRACT = {A new numerical technique for solving generalized Sturm--Liouville problem <i>d<sup>2</sup>w/dx<sup>2</sup> + q(x, λ )w</i> = 0, <i>b<sub>l</sub>[ λ ,w(a)]</i> = <i>b<sub>r</sub>[ λ ,w(b)]</i> = 0 is presented. In  is presented. In particular, we consider the problems when the coefficient <i>q(x, λ)</i> 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.},
DOI = {10.3970/cmes.2008.034.227}
}