High-order symplectic partitioned Lie group methods

DOI10.1007/s10208-015-9257-9zbMath1346.65069arXiv1303.5654OpenAlexW1552636115WikidataQ115385141 ScholiaQ115385141MaRDI QIDQ285442

Håkon Marthinsen, Geir Bogfjellmo

Publication date: 19 May 2016

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.5654

zbMATH Keywords

Hamiltonian systemsymplectic integratorsvariational integratorsorder theoryCrouch-Grossman schemesLie group methodsRunge-Kutta-Munthe-Kaas methods

Mathematics Subject Classification ID

Variational methods for problems in mechanics (70G75) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Hamiltonian and Lagrangian mechanics (70Hxx)

Related Items (12)

Lie group integrators for mechanical systems ⋮ Variational order for forced Lagrangian systems ⋮ Retraction maps: a seed of geometric integrators ⋮ B-stability of numerical integrators on Riemannian manifolds ⋮ Lie-Poisson methods for isospectral flows ⋮ The integration of angular velocity ⋮ Variational order for forced Lagrangian systems II. Euler–Poincaré equations with forcing ⋮ Galerkin Lie-group variational integrators based on unit quaternion interpolation ⋮ Lie group spectral variational integrators ⋮ High-order symplectic Lie group methods on \(SO(n)\) using the polar decomposition ⋮ High-order integrators for Lagrangian systems on homogeneous spaces via nonholonomic mechanics ⋮ Variational symplectic diagonally implicit Runge-Kutta methods for isospectral systems

Uses Software

• DiffMan

Cites Work

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