Conservative Methods for Dynamical Systems

DOI10.1137/16M110719XzbMath1375.65104arXiv1612.02417OpenAlexW3101986942MaRDI QIDQ5359497

Jean-Christophe Nave, Alexander Bihlo, Andy T. S. Wan

Publication date: 25 September 2017

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.02417

zbMATH Keywords

three-body problemdynamical systemconservative methodsLotka-Volterra systemsfinite differencelong-term stabilityEuler's equationnonautonomousfirst integralmultiplier methoddivided differencedamped harmonic oscillatorconserved quantityrigid body rotationautonomousquasi-linear system

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Two-body problems (70F05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Finite difference and finite volume methods for ordinary differential equations (65L12) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (10)

Conservative integrators for many-body problems ⋮ Conservative integrators for vortex blob methods on the plane ⋮ Invariant variational schemes for ordinary differential equations ⋮ Birational maps from polarization and the preservation of measure and integrals ⋮ On the development of symmetry-preserving finite element schemes for ordinary differential equations ⋮ On the design of non-singular, energy-momentum consistent integrators for nonlinear dynamics using energy splitting and perturbation techniques ⋮ Conservative integrators for piecewise smooth systems with transversal dynamics ⋮ On the Arbitrarily Long-Term Stability of Conservative Methods ⋮ Linear gradient structures and discrete gradient methods for conservative/dissipative differential-algebraic equations ⋮ Symmetry-Preserving Finite Element Schemes: An Introductory Investigation

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