The tau method and a new preconditioner.

DOI10.1016/j.cam.2003.04.001zbMath1046.65060OpenAlexW2807920410MaRDI QIDQ1428084

Farideh Ghoreishi, Mohammed Hosseini Ali Abadi

Publication date: 14 March 2004

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

Full work available at URL: https://doi.org/10.1016/j.cam.2003.04.001

zbMATH Keywords

preconditionersLegendre polynomialGegenbauer polynomialChebyshev polynomialtau methodnumerical result

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical computation of matrix norms, conditioning, scaling (65F35) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (7)

A Generic and Strictly Banded Spectral Petrov–Galerkin Method for Differential Equations with Polynomial Coefficients ⋮ The adaptive operational tau method for systems of ODEs ⋮ The performance of a Tau preconditioner on systems of ODEs ⋮ A new collocation scheme using non-polynomial basis functions ⋮ Integration matrix based on arbitrary grids with a preconditioner for pseudospectral method ⋮ Efficient Chebyshev-Petrov-Galerkin method for solving second-order equations ⋮ A new recursive formulation of the Tau method for solving linear Abel-Volterra integral equations and its application to fractional differential equations

Cites Work

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• An operational approach to the Tau method for the numerical solution of non-linear differential equations
• Linear operator theory in engineering and science. Repr. of the 1971 orig., publ. by Holt, Rinehart \& Winston, Inc.
• The origin and nature of spurious eigenvalues in the spectral tau method
• Numerical Solution of Stiff and Singularly Perturbed Boundary Value Problems With a Segmented-Adaptive Formulation of the Tau Method
• A Unified View of Some Methods for Stiff Two-Point Boundary Value Problems
• Integration Preconditioning of Pseudospectral Operators. I. Basic Linear Operators
• A Preconditioning of the Tau Operator for Ordinary Differential Equations
• An efficient spectral method for ordinary differential equations with rational function coefficients
• The Tau Method

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