On spectral approximations in elliptical geometries using Mathieu functions

DOI10.1090/S0025-5718-08-02197-2zbMath1198.65236OpenAlexW2056244731MaRDI QIDQ3055121

Jie Shen, Li-Lian Wang

Publication date: 7 November 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-08-02197-2

zbMATH Keywords

Helmholtz equationselliptic coordinatesMathieu functionsapproximation in Sobolev spaces

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (9)

Dirichlet-to-Neumann mappings and finite-differences for anisotropic diffusion ⋮ Spectral collocation solutions to multiparameter Mathieu's system ⋮ Periodized radial basis functions. I: Theory. ⋮ An improved estimate of PSWF approximation and approximation by Mathieu functions ⋮ Some progress in spectral methods ⋮ Computation and Applications of Mathieu Functions: A Historical Perspective ⋮ A new generalization of the PSWFs with applications to spectral approximations on quasi-uniform grids ⋮ Reprint of: ``Dirichlet-to-Neumann mappings and finite-differences for anisotropic diffusion ⋮ Optimized Schwarz methods with elliptical domain decompositions

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