Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems
Classical Analysis and ODEs
2014-08-21 v3 Mathematical Physics
Functional Analysis
math.MP
Numerical Analysis
Abstract
A method for approximate solution of spectral problems for Sturm-Liouville equations based on the construction of the Delsarte transmutation operators is presented. In fact the problem of numerical approximation of solutions and eigenvalues is reduced to approximation of a primitive of the potential by a finite linear combination of generalized wave polynomials introduced in arXiv:1208.5984, arXiv:1208.6166. The method allows one to compute both lower and higher eigendata with an extreme accuracy.
Keywords
Cite
@article{arxiv.1306.2914,
title = {Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems},
author = {Vladislav V. Kravchenko and Sergii M. Torba},
journal= {arXiv preprint arXiv:1306.2914},
year = {2014}
}
Comments
32 pages, 9 figures, 4 tables; Sections 6 and 7 extended, runtimes added