Multidomain spectral method for the Gauss hypergeometric function

DOI10.1007/s11075-019-00741-7zbMath1462.65092arXiv1809.10422OpenAlexW2963679794MaRDI QIDQ2181638

S. Crespo, Christian Klein, Nikola M. Stoilov, Marco Fasondini, Claude Vallee

Publication date: 19 May 2020

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.10422

zbMATH Keywords

hypergeometric functionspectral methodssingular differential equations

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (7)

Multi-domain spectral approach with Sommerfeld condition for the Maxwell equations ⋮ Numerical approach to Painlevé transcendents on unbounded domains ⋮ One answer to an open problem on the monotonicity of Gaussian hypergeometric functions with respect to parameters ⋮ Orthogonal polynomials on planar cubic curves ⋮ The numerical solution of fractional integral equations via orthogonal polynomials in fractional powers ⋮ Multi-domain spectral approach for the Hilbert transform on the real line ⋮ Numerical scattering for the defocusing Davey–Stewartson II equation for initial data with compact support

Uses Software

• Matlab
• DLMF
• Chebfun
• Differentiation Matrix Suite

Cites Work

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• Numerical methods for the computation of the confluent and Gauss hypergeometric functions
• A numerical methodology for the Painlevé equations
• Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions
• Two results on polynomial interpolation in equally spaced points
• Numerical approach to Painlevé transcendents on unbounded domains
• On the numerical solution of some semilinear elliptic problems
• Computational approach to hyperelliptic Riemann surfaces
• On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation
• A Fast and Well-Conditioned Spectral Method
• Computational approach to compact Riemann surfaces
• Spectral Methods in MATLAB
• Barycentric Lagrange Interpolation
• Computing with Functions in Spherical and Polar Geometries II. The Disk

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