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

作者：Reutskiy S Yu^*

来源：Computer Modeling in Engineering & Sciences, 2008, 34(3): 227-252.

• Non-linear eigenvalue problems
• Singular Sturm-Liouville problems
• Numerical solution
• Periodic eigenvalue problems
• Parameter-dependent boundary conditions

A new numerical technique for solving generalized Sturm-Liouville problem d(2)w/dx(2) + q(x, lambda)w = 0, b(l) [lambda, w(a)] = b, [lambda, w(b)] = 0 is presented. in particular, we consider the problems when the coefficient q(x, lambda) or the boundary conditions depend on the spectral parameter lambda 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.

• 出版日期2008-9