Discrete gradient methods for preserving a first integral of an ordinary differential equation

DOI10.3934/dcds.2014.34.1147zbMath1278.65104arXiv1301.4717OpenAlexW2963544807MaRDI QIDQ379795

Richard A. Norton, Gilles Reinout Willem Quispel

Publication date: 11 November 2013

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.4717

zbMATH Keywords

numerical exampleerror boundsHamiltonian systemsgeometric integrationlinearly implicit methodsorder of accuracydiscrete gradientsenergy preserving integrators

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (5)

Conservative Methods for Dynamical Systems ⋮ Projection methods and discrete gradient methods for preserving first integrals of ODEs ⋮ Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations ⋮ Order theory for discrete gradient methods ⋮ Discrete gradient methods and linear projection methods for preserving a conserved quantity of stochastic differential equations

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• Solving ODEs numerically while preserving a first integral

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