On the Abramov approach for the approximation of whispering gallery modes in prolate spheroids

Pierluigi Amodio, Anton Arnold, Tatiana Levitina, Giuseppina Settanni and Ewa B. Weinmüller

Applied Mathematics and Computation, 2021, vol. 409, issue C

Abstract: In this paper, we present the Abramov approach for the numerical simulation of the whispering gallery modes in prolate spheroids. The main idea of this approach is the Newton–Raphson technique combined with the quasi-time marching. In the first step, a solution of a simpler problem, as an initial guess for the Newton–Raphson iterations, is provided. Then, step-by-step, this simpler problem is converted into the original problem, while the quasi-time parameter τ runs from τ=0 to τ=1. While following the involved imaginary path two numerical approaches are realized, the first is based on the Prüfer angle technique, the second on high order finite difference schemes.

Keywords: Separation of variables; ‘Whispering gallery’ mode; Multi-parameter spectral problems; Prüfer angle; High accuracy finite differences (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300320305543
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300320305543

DOI: 10.1016/j.amc.2020.125599

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().