# Analysis of Energy and QUadratic Invariant Preserving (EQUIP) methods

## TL;DR

This paper analyzes EQUIP methods, a class of geometric integrators that conserve energy and quadratic invariants, providing reformulation, refined analysis, and numerical comparisons with Gauss methods.

## Contribution

It offers a reformulation and detailed analysis of EQUIP methods, including a practical implementation procedure and comparative numerical tests.

## Key findings

- EQUIP methods conserve Hamiltonian and quadratic invariants.
- Numerical tests show EQUIP methods' effectiveness on Hamiltonian problems.
- Comparison indicates advantages over traditional Gauss 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.