On construction of transmutation operators for perturbed Bessel equations
Classical Analysis and ODEs
2017-12-06 v1 Mathematical Physics
math.MP
Abstract
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure. New properties of the transmutation kernel are established. A new representation of the regular solution of the perturbed Bessel equation is given presenting a remarkable feature of uniform error bound with respect to the spectral parameter for partial sums of the series. A numerical illustration of application to the solution of Dirichlet spectral problems is presented.
Cite
@article{arxiv.1712.01363,
title = {On construction of transmutation operators for perturbed Bessel equations},
author = {Vladislav V. Kravchenko and Elina L. Shishkina and Sergii M. Torba},
journal= {arXiv preprint arXiv:1712.01363},
year = {2017}
}
Comments
16 pages, 3 figures