Numerical simulation of the whispering gallery modes in prolate spheroids

DOI10.1016/j.cpc.2013.12.012zbMath1344.35019OpenAlexW2160548498MaRDI QIDQ314067

T. V. Levitina, Pierluigi Amodio, Ewa B. Weinmüller, Giuseppina Settanni

Publication date: 12 September 2016

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2013.12.012

zbMATH Keywords

Prüfer angle`whispering gallery' modehigh order finite difference schemesmorphology dependent resonancesmulti-parameter spectral problems

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Second-order elliptic equations (35J15) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (9)

Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems ⋮ Reprint of ``Variable-step finite difference schemes for the solution of Sturm-Liouville problems ⋮ Numerical Strategies for Solving Multiparameter Spectral Problems ⋮ Computation of eigenfrequencies of an acoustic medium in a prolate spheroid by a modified Abramov method ⋮ Near critical, self-similar, blow-up solutions of the generalised Korteweg-de Vries equation: asymptotics and computations ⋮ On the Abramov approach for the approximation of whispering gallery modes in prolate spheroids ⋮ Mathematical Aspects Relative to the Fluid Statics of a Self-Gravitating Perfect-Gas Isothermal Sphere ⋮ Fluid statics of a self-gravitating perfect-gas isothermal sphere ⋮ Variable-step finite difference schemes for the solution of Sturm-Liouville problems

Uses Software

• HOFiD_UP

Cites Work

• A finite differences MATLAB code for the numerical solution of second order singular perturbation problems
• Multiparameter eigenvalue problems and expansion theorems
• A method for solving selfadjoint multiparameter spectral problems for weakly coupled sets of ordinary differential equations
• On the calculation of the finite Hankel transform eigenfunctions
• Evaluation of Lamé angular wave functions by solving auxiliary differential equations
• Multiparameter spectral theory and separation of variables
• Evaluation of prolate spheroidal function by solving the corresponding differential equations
• A numerical solution to some three-parameter spectral problems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Numerical simulation of the whispering gallery modes in prolate spheroids