Asymptotic behaviors and numerical computations of the eigenfunctions and eigenvalues associated with the classical and circular prolate spheroidal wave functions

DOI10.1016/j.amc.2012.04.048zbMath1280.33017OpenAlexW2013805338MaRDI QIDQ387453

Issam Mehrzi, Abderrazek Karoui

Publication date: 23 December 2013

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2012.04.048

zbMATH Keywords

asymptotic behaviororthogonal polynomialseigenvalueseigenfunctionsBessel functionsWKB methodquadrature methodsprolate spheroidal wave functions

Mathematics Subject Classification ID

Lamé, Mathieu, and spheroidal wave functions (33E10) Numerical approximation and evaluation of special functions (33F05)

Related Items (2)

The finite Hankel transform operator: some explicit and local estimates of the eigenfunctions and eigenvalues decay rates ⋮ The nonconvergence of \(h\)-refinement in prolate elements

Cites Work

• Pseudospectral method based on prolate spheroidal wave functions for semiconductor nanodevice simulation
• A new generalization of the PSWFs with applications to spectral approximations on quasi-uniform grids
• Spectral analysis of the finite Hankel transform and circular prolate spheroidal wave functions
• Approximation of an analytic function on a finite real interval by a bandlimited function and conjectures on properties of prolate spheroidal functions
• Prolate spheroidal wave functions, an introduction to the Slepian series and its properties
• On generalized Gaussian quadratures for exponentials and their applications
• Prolate spheroidal wavefunctions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudospectral algorithms
• New efficient methods of computing the prolate spheroidal wave functions and their corresponding eigenvalues
• An improved estimate of PSWF approximation and approximation by Mathieu functions
• A new friendly method of computing prolate spheroidal wave functions and wavelets
• Analysis of spectral approximations using prolate spheroidal wave functions
• Some Asymptotic Expansions for Prolate Spheroidal Wave Functions
• Spectral Methods Based on Prolate Spheroidal Wave Functions for Hyperbolic PDEs
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - II
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions
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