Pseudo-symplectic Runge-Kutta methods

DOI10.1007/BF02510253zbMath0916.65084OpenAlexW2060128171MaRDI QIDQ1272872

K. Appert

Publication date: 7 March 1999

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02510253

zbMATH Keywords

numerical experimentsHamiltonian systemssymplectic Runge-Kutta methodspseudo-symplecticness conditionspseudosymplectic Runge Kutta methods

Mathematics Subject Classification ID

Hamilton's equations (70H05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (25)

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Cites Work

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• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Almost Poisson integration of rigid body systems
• Canonical \(B\)-series
• The life-span of backward error analysis for numerical integrators
• The Development of Variable-Step Symplectic Integrators, with Application to the Two-Body Problem
• Solving Ordinary Differential Equations I
• High-Order Symplectic Runge–Kutta–Nyström Methods

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