Forced extension of GNI techniques to dissipative systems

TL;DR

This paper introduces a novel approach to handle dissipative systems by extending GNI techniques through a new energy reservoir concept, with numerical experiments demonstrating qualitative effectiveness despite accuracy challenges.

Contribution

It presents a new theoretical framework for dissipative systems using energy reservoirs within GNI, supported by initial numerical validation.

Findings

Qualitative behavior of the integration technique is promising.

Rising accuracy remains challenging due to dissipation.

Numerical experiments support the potential of the approach.

Abstract

We propose new concept of energy reservoir and effectively conserved quantity, what enables us to treat dissipative systems along the lines of the framework of Geometric Numerical Integration. Using this opportunity, we try to confirm numerically if our idea is useful. Numerical experiments show good qualitative behavior of integration technique for ODEs based on non-potential Hamiltonian formalism. It occurs that rising accurracy is a difficult task due to dissipative form of the system under scrutiny.