Spectral parameter power series for Sturm-Liouville problems
Abstract
We consider a recently discovered representation for the general solution of the Sturm-Liouville equation as a spectral parameter power series (SPPS). The coefficients of the power series are given in terms of a particular solution of the Sturm-Liouville equation with the zero spectral parameter. We show that, among other possible applications, this provides a new and efficient numerical method for solving initial value and boundary value problems. Moreover, due to its convenient form the representation lends itself to numerical solution of spectral Sturm-Liouville problems, effectively by calculation of the roots of a polynomial. We discuss examples of the numerical implementation of the SPPS method and show it to be equally applicable to a wide class of singular Sturm-Liouville problems as well as to problems with spectral parameter dependent boundary conditions.
Cite
@article{arxiv.0811.4488,
title = {Spectral parameter power series for Sturm-Liouville problems},
author = {Vladislav V. Kravchenko and R. Michael Porter},
journal= {arXiv preprint arXiv:0811.4488},
year = {2011}
}