Functionally-fitted energy-preserving integrators for Poisson systems
arXiv:1712.06084 · doi:10.1016/j.jcp.2018.03.015
Abstract
In this paper, a new class of energy-preserving integrators is proposed and analysed for Poisson systems by using functionally-fitted technology. The integrators exactly preserve energy and have arbitrarily high order. It is shown that the proposed approach allows us to obtain the energy-preserving methods derived in BIT 51 (2011) by Cohen and Hairer and in J. Comput. Appl. Math. 236 (2012) by Brugnano et al. for Poisson systems. Furthermore, we study the sufficient conditions that ensure the existence of a unique solution and discuss the order of the new energy-preserving integrators.
19 pages
References in corpus (3)
- Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems
- Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations
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Cited by in corpus (5)
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- Arbitrary high-order methods for one-sided direct event location in discontinuous differential problems with nonlinear event function
- Arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation
- Energy-preserving integration of non-canonical Hamiltonian systems by continuous-stage methods