A class of collocation methods for numerical integration of initial value problems

DOI10.1016/j.camwa.2011.08.036zbMath1232.65113OpenAlexW1971068722MaRDI QIDQ662242

Anna Napoli, Francesco Aldo Costabile

Publication date: 21 February 2012

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.08.036

zbMATH Keywords

initial value problemcollocation methods

Mathematics Subject Classification ID

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

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An innovative harmonic numbers operational matrix method for solving initial value problems ⋮ Generalized Runge-Kutta method with respect to the non-Newtonian calculus ⋮ A class of Birkhoff-Lagrange-collocation methods for high order boundary value problems ⋮ Unnamed Item ⋮ Solutions of linear second order initial value problems by using Bernoulli polynomials ⋮ (Spectral) Chebyshev collocation methods for solving differential equations ⋮ \(\Delta_h\)-Appell sequences and related interpolation problem ⋮ Unnamed Item ⋮ Collocation for high order differential equations with two-points Hermite boundary conditions ⋮ A unified approach for solving linear and nonlinear odd-order two-point boundary value problems ⋮ A novel class of collocation methods based on the weighted integral form of ODEs ⋮ Collocation for high-order differential equations with Lidstone boundary conditions ⋮ Lidstone-Euler interpolation and related high even order boundary value problem ⋮ Odd and even Lidstone-type polynomial sequences. II: Applications ⋮ A method for high-order multipoint boundary value problems with Birkhoff-type conditions ⋮ Numerical solution of high order Bernoulli boundary value problems

Cites Work

• A family of implicit Chebyshev methods for the numerical integration of second-order differential equations
• Stability of Chebyshev collocation methods
• The Chebyshev methods of Panovsky and Richardson as Runge-Kutta-Nyström methods
• Collocation at Gaussian Points
• Chebyshev Collocation Methods for Ordinary Differential Equations
• A method for global approximation of the initial value problem
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