TY  - EJOU
AU  - Reutskiy, S.Yu. 

TI  - A Meshless Method for Nonlinear, Singular and Generalized Sturm-Liouville Problems
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2008
VL  - 34
IS  - 3
SN  - 1526-1506

AB  - 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.
KW  - Non-linear eigenvalue problems
KW  -  Singular Sturm--Liouville problems
KW  -  Numerical solution
KW  -  Periodic eigenvalue problems
KW  -  Parameter-dependent boundary conditions

DO  - 10.3970/cmes.2008.034.227