Geometric integration methods that unconditionally contract volume

DOI10.1016/j.apnum.2007.04.018zbMath1143.65056OpenAlexW1983838979MaRDI QIDQ932778

Gilles Reinout Willem Quispel, Volker Grimm

Publication date: 11 July 2008

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2007.04.018

zbMATH Keywords

numerical examplesprojection methodRunge-Kutta methodgeometric integrationsplitting methodvolume-preserving system

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (1)

Computational geometric methods for preferential clustering of particle suspensions

Cites Work

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• Volume-preserving schemes and numerical experiments
• Generating functions for volume-preserving mappings and Hamilton-Jacobi equations for source-free dynamical systems
• Numerical integrators that contract volume
• Volume-preserving algorithms for source-free dynamical systems
• Geometric integration methods that preserve Lyapunov functions
• Simulating Hamiltonian Dynamics
• Splitting methods
• Stability Criteria for Implicit Runge–Kutta Methods
• A necessary condition forB-stability
• Geometric integrators for ODEs
• Geometric Numerical Integration
• Volume-preserving integrators

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