Arbitrarily high-order energy-conserving methods for Hamiltonian problems with quadratic holonomic constraints

TL;DR

This paper introduces a new class of high-order energy-conserving numerical methods for Hamiltonian systems with quadratic holonomic constraints, using a line integral framework, supported by numerical validation.

Contribution

It develops arbitrarily high-order methods that exactly conserve energy for constrained Hamiltonian systems, a novel approach within the line integral framework.

Findings

Methods achieve high-order accuracy

Energy conservation is verified numerically

Applicable to systems with quadratic holonomic constraints

Abstract

In this paper, we define arbitrarily high-order energy-conserving methods for Hamiltonian systems with quadratic holonomic constraints. The derivation of the methods is made within the so-called line integral framework. Numerical tests to illustrate the theoretical findings are presented.