The Tau method as an analytic tool in the discussion of equivalence results across numerical methods

DOI10.1007/BF02684381zbMath0908.65072MaRDI QIDQ1265396

Eduardo L. Ortiz, Mohamed K. El-Daou

Publication date: 1998

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

finite difference methodscollocationspectral methodsTau method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (9)

A posteriori error bounds for the approximate solution of second-order ODEs by piecewise coefficients perturbation methods ⋮ Segmented tau approximation for test neutral functional differential equations ⋮ Tensor calculus in spherical coordinates using Jacobi polynomials. I: Mathematical analysis and derivations ⋮ Parallel strategies for the step by step tau method ⋮ Segmented tau approximation for a forward-backward functional differential equation ⋮ Exponentially weighted Legendre-Gauss tau methods for linear second-order differential equations ⋮ Orthogonal collocation revisited ⋮ Computation of the canonical polynomials and applications to some optimal control problems ⋮ Numerical computation of the tau approximation for the Volterra-Hammerstein integral equations

Uses Software

• RODAS

Cites Work

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• Perturbed collocation and Runge-Kutta methods
• A recursive formulation of collocation in terms of canonical polynomials
• A unified approach to the tau method and Chebyshev series expansion techniques
• On One-Leg Multistep Methods
• Numerical Solution of Stiff and Singularly Perturbed Boundary Value Problems With a Segmented-Adaptive Formulation of the Tau Method
• Superconvergence for Multistep Collocation
• The Tau Method
• Some relationships between implicit Runge-Kutta, collocation and Lanczosτ methods, and their stability properties
• Trigonometric Interpolation of Empirical and Analytical Functions

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