Spectral parameter power series method for discontinuous coefficients
Mathematical Physics
2023-07-19 v2 Classical Analysis and ODEs
math.MP
Abstract
Let (a,b) be a finite interval and 1/p, q, r be functions from L1(a,b). We show that a general solution (in the weak sense) of the equation (pu')'+qu = zru on (a,b) can be constructed in terms of power series of the spectral parameter z. The series converge uniformly on [a,b] and the corresponding coefficients are constructed by means of a simple recursive procedure. We use this representation to solve different types of eigenvalue problems. Several numerical tests are discussed.
Cite
@article{arxiv.1405.5632,
title = {Spectral parameter power series method for discontinuous coefficients},
author = {Herminio Blancarte and Hugo M. Campos and Kira V. Khmelnytskaya},
journal= {arXiv preprint arXiv:1405.5632},
year = {2023}
}