Anzeige
Erschienen in:
01.06.2015
On the positivity of Poisson integrators for the Lotka–Volterra equations
Erschienen in: BIT Numerical Mathematics | Ausgabe 2/2015
EinloggenAktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
Over the last decade, the field of geometric integration has rapidly established itself as one of the core research areas in numerical ordinary differential equations. Geometric integrators are numerical methods which preserve some of the mathematical or physical properties of the system they are approximating. In the case of the Lotka–Volterra equations, which are a Poisson system, a good geometric integrator should also be a Poisson integrator. There is however another important property of solutions of the Lotka–Volterra equations: they are non-negative, since they represent population densities. We study in this paper the conditions under which two Poisson integrators for the Lotka–Volterra equations lead to positive approximate solutions.