On the connection coefficients for linear differential systems with applications to the spheroidal and ellipsoidal wave equation

Autor:	Schmid, Harald
Rok vydání:	2023
Předmět:	Mathematics - Classical Analysis and ODEs Mathematical Physics Mathematics - Numerical Analysis 33E10 33F05 34L16 65D20
Zdroj:	Mathematics and Computers in Simulation, 2024
Druh dokumentu:	Working Paper
DOI:	10.1016/j.matcom.2024.05.028
Popis:	This paper is concerned with the connection coefficients between the local fundamental solutions of a $2\times 2$ linear ordinary differential system with two neighboring regular singular points at $z=0$ and $z=1$. We derive an asymptotic formula for the connection coefficients which can be used for numerical calculations and, in particular, for determining the eigenvalues of some spectral problems arising in mathematical physics. As an application, new algorithms for computing the eigenvalues of the ellipsoidal wave equation and the spheroidal wave equation are presented. Comment: 20 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.06511 Zobrazit plný text záznamu View this record from Arxiv