Analysis of Energy and QUadratic Invariant Preserving (EQUIP) methods

Abstract

In this paper we are concerned with the analysis of a class of geometric integrators, at first devised in [14, 18], which can be regarded as an energy-conserving variant of Gauss collocation methods. With these latter they share the property of conserving quadratic first integrals but, in addition, they also conserve the Hamiltonian function itself. We here reformulate the methods in a more convenient way, and propose a more refined analysis than that given in [18] also providing, as a by-product, a practical procedure for their implementation. A thorough comparison with the original Gauss methods is carried out by means of a few numerical tests solving Hamiltonian and Poisson problems.

arXiv comment28 pages, 2 figures, 4 tables

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• A note on the continuous-stage Runge-Kutta-(Nyström) formulation of Hamiltonian Boundary Value Methods (HBVMs)
• Arbitrarily high-order energy-conserving methods for Poisson problems
• Drift-preserving numerical integrators for stochastic Poisson systems
• Energy-preserving multi-symplectic Runge-Kutta methods for Hamiltonian wave equations
• Two novel classes of arbitrary high-order structure-preserving algorithms for canonical Hamiltonian systems
• Arbitrary high-order methods for one-sided direct event location in discontinuous differential problems with nonlinear event function