Speaker: Elena Celledoni
Norwegian University of Science and Technology Trondheim, Norway
Title: Energy-preserving integrators and B-series
Abstract: This talk will be concerned with numerical integrators that preserve first integrals of differential equations exactly, in particular energy-preserving integrators. The preferred method to preserve first integrals of differential equations is the Discrete Gradient Method. This method relies on the construction of a so-called discrete gradient of the first integral, and requires the user to know and input the first integral to be preserved. The average vector field method is an integration method which belongs to this class but also to the class of so-called B-series methods. These are methods which have an associated Lie algebra of energy-preserving linear combinations of elementary differentials, much like symplectic B- series methods have an associated Lie algebra of Hamiltonian linear combinations of elementary differentials. We have characterized the linear subspaces of energy-preserving (EP) and Hamiltonian modified vector fields which admit a B-series, their finite-dimensional truncations, and their annihilators. We have also studied the manifolds of B-series conjugate to Hamiltonian and conjugate to energy- preserving.