Preserving first integrals with symmetric Lie group methods

DOI10.3934/dcds.2014.34.977zbMath1278.65097arXiv1302.4702OpenAlexW2963516565MaRDI QIDQ379774

Brynjulf Owren, Elena Celledoni

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/1302.4702

zbMATH Keywords

Lie group methodsdiscrete gradient approachpreservation of first integrals

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Nonlinear ordinary differential equations and systems (34A34) Applications of Lie groups to the sciences; explicit representations (22E70) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items

Dissipative Numerical Schemes on Riemannian Manifolds with Applications to Gradient Flows, Linear gradient structures and discrete gradient methods for conservative/dissipative differential-algebraic equations, Energy-preserving methods on Riemannian manifolds, The Magnus expansion for stochastic differential equations, Variational Image Regularization with Euler's Elastica Using a Discrete Gradient Scheme, Energy-preserving integrators applied to nonholonomic systems

Cites Work

• Unnamed Item
• Unnamed Item
• Linear energy-preserving integrators for Poisson systems
• An introduction to Lie group integrators - basics, new developments and applications
• Conserving algorithms for the dynamics of Hamiltonian systems on Lie groups
• Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
• Time integration and discrete Hamiltonian systems
• Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
• Topics in structure-preserving discretization
• A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
• Newton's method on Riemannian manifolds and a geometric model for the human spine
• Nonlinear stability of rotating pseudo-rigid bodies
• Geometric integration using discrete gradients
• Collocation and Relaxed Collocation for the Fer and the Magnus Expansions