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BIT Numerical Mathematics

, Volume 45, Issue 4, pp 709–723 | Cite as

Geometric Integration Methods that Preserve Lyapunov Functions

  • V. Grimm
  • G. R. W. Quispel
Article

Abstract

We consider ordinary differential equations (ODEs) with a known Lyapunov function V. To ensure that a numerical integrator reflects the correct dynamical behaviour of the system, the numerical integrator should have V as a discrete Lyapunov function. Only second-order geometric integrators of this type are known for arbitrary Lyapunov functions. In this paper we describe projection-based methods of arbitrary order that preserve any given Lyapunov function.

Key words

geometric integration Lyapunov function Runge-Kutta methods numerical solution 

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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of Mathematics, and Centre for Mathematics and Statistics of Complex SystemsLa Trobe UniversityBundooraAustralia

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