Two-step almost collocation methods for ordinary differential equations

DOI10.1007/s11075-009-9280-5zbMath1186.65107OpenAlexW1972053220MaRDI QIDQ849272

M. Ferro, Raffaele D'Ambrosio, Beatrice Paternoster, Zdzisław Jackiewicz

Publication date: 25 February 2010

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-009-9280-5

zbMATH Keywords

absolute stabilityinitial value problem\(A\)-stabilityorder conditionslocal error estimationtwo-step collocation methodssystem of nonlinear ordinary differential equations

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (25)

Construction and implementation of two-step continuous methods for Volterra integral equations ⋮ A class of two-step collocation methods for Volterra integro-differential equations ⋮ Second derivative two-step collocation methods for ordinary differential equations ⋮ Variable stepsize multivalue collocation methods ⋮ Explicit Nordsieck methods with quadratic stability ⋮ Collocation–Based Two Step Runge–Kutta Methods for Ordinary Differential Equations ⋮ Trigonometrically fitted two-step hybrid methods for special second order ordinary differential equations ⋮ Multistep collocation methods for Volterra integro-differential equations ⋮ Exponentially fitted two-step Runge-Kutta methods: construction and parameter selection ⋮ Two-step diagonally-implicit collocation based methods for Volterra integral equations ⋮ Two-step modified collocation methods with structured coefficient matrices ⋮ Numerical integration of Hamiltonian problems by G-symplectic methods ⋮ Multivalue collocation methods free from order reduction ⋮ Order conditions for general linear Nyström methods ⋮ A block hybrid method for non-linear second order boundary value problems ⋮ Parallel methods for weakly singular Volterra integral equations on GPUs ⋮ Search for efficient general linear methods for ordinary differential equations ⋮ \(P\)-stable general Nyström methods for \(y=f(y(t))\) ⋮ Exponentially fitted singly diagonally implicit Runge-Kutta methods ⋮ Continuous two-step Runge-Kutta methods for ordinary differential equations ⋮ Construction and implementation of highly stable two-step continuous methods for stiff differential systems ⋮ GPU-acceleration of waveform relaxation methods for large differential systems ⋮ Two-step almost collocation methods for Volterra integral equations ⋮ Multivalue second derivative collocation methods ⋮ Nested second derivative two-step Runge-Kutta methods

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