Explicit volume-preserving and symplectic integrators for trigonometric polynomial flows
Journal of Computational Physics
Lie group foliations: dynamical systems and integrators
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
Linear Stability of Partitioned Runge-Kutta Methods
SIAM Journal on Numerical Analysis
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We consider properties of flows, the relationships between them, and whether numerical integrators can be made to preserve these properties. This is done in the context of automorphisms and antiautomorphisms of a certain group generated by maps associated to vector fields. This new framework unifies several known constructions. We also use the concept of "covariance" of a numerical method with respect to a group of coordinate transformations. The main application is to explore the relationship between spatial symmetries, reversing symmetries, and time symmetry of flows and numerical integrators.