Linear energy-preserving integrators for Poisson systems
Journal article, 2011
For Hamiltonian systems with non-canonical structure matrix a new class of numerical integrators is proposed. The methods exactly preserve energy, are invariant with respect to linear transformations, and have arbitrarily high order. Those of optimal order also preserve quadratic Casimir functions. The discussion of the order is based on an interpretation as partitioned Runge-Kutta method with infinitely many stages.
Partitioned Runge-Kutta method
Poisson system
Gaussian quadrature
Collocation
Energy preservation
Casimir function
Author
David Cohen
University of Basel
Ernst Hairer
University of Geneva
BIT Numerical Mathematics
0006-3835 (ISSN) 1572-9125 (eISSN)
Vol. 51 1 91-101Subject Categories
Mathematics
DOI
10.1007/s10543-011-0310-z