Journal
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
Volume 10, Issue 6, Pages 673-693Publisher
SPRINGER
DOI: 10.1007/s10208-010-9073-1
Keywords
B-series methods; Symplectic integration; Energy preservation; Trees; Conjugate methods
Funding
- Royal Society of New Zealand
- Australian Research Council
- Norwegian Research Council
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B-series are a powerful tool in the analysis of Runge-Kutta numerical integrators and some of their generalizations (B-series methods). A general goal is to understand what structure-preservation can be achieved with B-series and to design practical numerical methods that preserve such structures. B-series of Hamiltonian vector fields have a rich algebraic structure that arises naturally in the study of symplectic or energy-preserving B-series methods and is developed in detail here. We study the linear subspaces of energy-preserving and Hamiltonian modified vector fields which admit a B-series, their finite-dimensional truncations, and their annihilators. We characterize the manifolds of B-series that are conjugate to Hamiltonian and conjugate to energy-preserving and describe the relationships of all these spaces.
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