Analysis of Energy and QUadratic Invariant Preserving (EQUIP) methods
For researchers in geometric numerical integration, this work offers improved energy-conserving integrators for Hamiltonian and Poisson systems.
The paper analyzes a class of geometric integrators that conserve both energy and quadratic invariants, providing a refined analysis and practical implementation procedure. Numerical tests show these methods outperform standard Gauss collocation in preserving Hamiltonian structure.
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.