Spectrum of the Jacobi Tau Approximation for the Second Derivative Operator

DOI10.1137/060665907zbMath1160.65326arXivmath/0607640OpenAlexW1969909878MaRDI QIDQ3614179

Marios Charalambides, Fabian Waleffe

Publication date: 16 March 2009

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607640

zbMATH Keywords

zeros of polynomialsdiffusion equationJacobi polynomialsGegenbauer polynomialsChebyshev tau methodGalerkin methodsspectral methodsLegendre tau methodstable polynomialsJacobi tau methodpositive pairsGegenbauer tau method

Mathematics Subject Classification ID

Heat equation (35K05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (11)

Optimal error estimates of the Legendre tau method for second-order differential equations ⋮ On shifted Jacobi spectral method for high-order multi-point boundary value problems ⋮ Spectral approximations of unbounded operators of the type ``normal plus compact ⋮ Spectral integration of linear boundary value problems ⋮ The spectrum of the Gegenbauer collocation approximation for the second derivative operator ⋮ A new property of a class of Koornwinder Laguerre polynomials ⋮ The EPS method: A new method for constructing pseudospectral derivative operators ⋮ On conjectures by Csordas, Charalambides and Waleffe ⋮ The distribution of zeros of a class of Jacobi polynomials ⋮ On symmetrizing the ultraspherical spectral method for self-adjoint problems ⋮ A general stability theorem with applications

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