Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
USSR Computational Mathematics and Mathematical Physics
Almost Poisson integration of rigid body systems
Journal of Computational Physics
Unitary integrators and applications to continuous orthonormalization techniques
SIAM Journal on Numerical Analysis
Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems
SIAM Journal on Numerical Analysis
Runge-Kutta type methods for orthogonal integration
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
On the Compuation of Lyapunov Exponents for Continuous Dynamical Systems
SIAM Journal on Numerical Analysis
Numerical solution of isospectral flows
Mathematics of Computation
Structure Preservation for Constrained Dynamics with Super Partitioned Additive Runge--Kutta Methods
SIAM Journal on Scientific Computing
On the numerical integration of orthogonal flows with Runge-Kutta methods
Journal of Computational and Applied Mathematics - Proceedings of the 8th international congress on computational and applied mathematics
A Changing-Chart Symplectic Algorithm for Rigid Bodies and Other Hamiltonian Systems on Manifolds
SIAM Journal on Scientific Computing
Numerical Integration of Lie--Poisson Systems While Preserving Coadjoint Orbits and Energy
SIAM Journal on Numerical Analysis
A Class of Intrinsic Schemes for Orthogonal Integration
SIAM Journal on Numerical Analysis
Computation of a few Lyapunov exponents for continuous and discrete dynamical systems
Applied Numerical Mathematics
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We consider the numerical integration of two types of systems of differential equations. We first consider Hamiltonian systems of differential equations with a Poisson structure. We show that symplectic Runge-Kutta methods preserve this structure when the Poisson tensor is constant. Using nonlinear changes of coordinates this structure can also be preserved for nonconstant Poisson tensors, as exemplified on the Euler equations for the free rigid body. We also consider orthogonal flows and the closely related class of isospectral flows. To numerically preserve the orthogonality property we take the approach of formulating an equivalent system of differential-algebraic equations (DAEs) and of integrating the system with a special combination of a particular class of Runge-Kutta methods. This approach requires only matrix-matrix products and can preserve geometric properties of the flow such as reversibility.