Forced extension of GNI techniques to dissipative systems

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.