Multistep methods integrating ordinary differential equations on manifolds

DOI10.1016/S0168-9274(01)00103-9zbMath0996.65073MaRDI QIDQ5954982

Hans Z. Munthe-Kaas, Arne Marthinsen, Stig Faltinsen

Publication date: 7 February 2002

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

zbMATH Keywords

Runge-Kutta methodsmultistep methodsnumerical comparisonsbackward differentiation formulaAdams-Moulton methodsLie group settinglinear methods

Mathematics Subject Classification ID

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 (6)

Methods for suspensions of passive and active filaments ⋮ Performance of implicit A-stable time integration methods for multibody system dynamics ⋮ A generalised drift-correcting time integration scheme for Brownian suspensions of rigid particles with arbitrary shape ⋮ BDF integrators for constrained mechanical systems on Lie groups ⋮ Unnamed Item ⋮ DiffMan: An object-oriented MATLAB toolbox for solving differential equations on manifolds

Uses Software

• DiffMan

Cites Work

• Unnamed Item
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• Symmetry types of periodic sequences
• Runge-Kutta methods adapted to manifolds and based on rigid frames
• Modeling and solution of some mechanical problems on Lie groups
• High order Runge-Kutta methods on manifolds
• Numerical integration of ordinary differential equations on manifolds
• Runge-Kutta methods on Lie groups
• Multistep methods on manifolds
• Solving Ordinary Differential Equations I
• Computations in a free Lie algebra
• Collocation and Relaxed Collocation for the Fer and the Magnus Expansions
• Simulation of ordinary differential equations on manifolds: some numerical experiments and verifications
• Numerical solution of isospectral flows
• Maximal reductions in the Baker–Hausdorff formula
• Interpolation in Lie Groups
• The Baker–Campbell–Hausdorff formula and nested commutator identities
• Integrals of nonlinear equations of evolution and solitary waves
• DiffMan: An object-oriented MATLAB toolbox for solving differential equations on manifolds

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