A recursive formulation of collocation in terms of canonical polynomials

DOI10.1007/BF02238075zbMath0797.65056MaRDI QIDQ1319047

Eduardo L. Ortiz, Mohamed K. El-Daou

Publication date: 3 May 1994

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

collocation methodnumerical examplesboundary value problemslinear differential operatorspolynomial coefficientstau methodcanonical polynomials

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) 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 (12)

A posteriori error bounds for the approximate solution of second-order ODEs by piecewise coefficients perturbation methods ⋮ The adaptive operational tau method for systems of ODEs ⋮ The weighting subspaces of the tau method and orthogonal collocation ⋮ Differential equations with locally perturbed coefficients: High order error estimates for function and derivative ⋮ The number of extrema of the error function of a class of methods for differential equations ⋮ Some remarks on structural relations between the tau method and the finite element method ⋮ Computation of the canonical polynomials and applications to some optimal control problems ⋮ An improved tau method for a class of Sturm-Liouville problems ⋮ Numerical piecewise approximate solution of Fredholm integro-differential equations by the tau method ⋮ The Tau method as an analytic tool in the discussion of equivalence results across numerical methods ⋮ A new tau-collocation method with fractional basis for solving weakly singular delay Volterra integro-differential equations ⋮ A recursive formulation of Galerkin's method in terms of the tau method: Bounded and unbounded domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An operational approach to the Tau method for the numerical solution of non-linear differential equations
• Error analysis of the Tau method: Dependence of the approximation error on the choice of perturbation term
• Differential equations with piecewise approximate coefficients: Discrete and continuous estimation for initial and boundary value problems
• A note on accurate estimations of the local truncation error of polynomial methods for differential equations
• Step by step tau method. I: Piecewise polynomial approximations
• Error analysis of the Tau method: Dependence of the error on the degree and on the length of the interval of approximation
• A unified approach to the tau method and Chebyshev series expansion techniques
• On the convergence of the Tau method for nonlinear differential equations of Riccati's type
• Numerical Solution of Stiff and Singularly Perturbed Boundary Value Problems With a Segmented-Adaptive Formulation of the Tau Method
• Computing the Inverse of the Chebyshev Collocation Derivative
• Chebyshev Polynomials in the Numerical Solution of Differential Equations
• The Tau Method
• Some relationships between implicit Runge-Kutta, collocation and Lanczosτ methods, and their stability properties
• Trigonometric Interpolation of Empirical and Analytical Functions

This page was built for publication: A recursive formulation of collocation in terms of canonical polynomials