Two-step modified collocation methods with structured coefficient matrices

DOI10.1016/j.apnum.2012.06.008zbMath1251.65115OpenAlexW2061986119MaRDI QIDQ450892

Raffaele D'Ambrosio, Beatrice Paternoster

Publication date: 26 September 2012

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2012.06.008

zbMATH Keywords

convergencenumerical resultsA-stabilitydiagonally implicit Runge-Kutta methodsL-stabilitytwo-step Runge-Kutta methodsalmost collocation methodssingly implicit Runge-Kutta methods

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (18)

Construction and implementation of two-step continuous methods for Volterra integral equations ⋮ A class of two-step collocation methods for Volterra integro-differential equations ⋮ Two-step collocation methods for fractional differential equations ⋮ Trigonometrically fitted multi-step Runge-Kutta methods for solving oscillatory initial value problems ⋮ Optimal Schwarz waveform relaxation for fractional diffusion-wave 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 ⋮ Numerical integration of Hamiltonian problems by G-symplectic methods ⋮ Multivalue collocation methods free from order reduction ⋮ Order conditions for general linear Nyström methods ⋮ Parallel methods for weakly singular Volterra integral equations on GPUs ⋮ \(P\)-stable general Nyström methods for \(y=f(y(t))\) ⋮ Exponentially fitted singly diagonally implicit Runge-Kutta methods ⋮ Construction and implementation of highly stable two-step continuous methods for stiff differential systems ⋮ GPU-acceleration of waveform relaxation methods for large differential systems ⋮ Collocation methods for Volterra integral and integro-differential equations: a review ⋮ Multivalue second derivative collocation methods

Uses Software

• RODAS

Cites Work

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