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.
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Communicated by Mechthild Thalhammer.
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Beck, M., Gander, M.J. On the positivity of Poisson integrators for the Lotka–Volterra equations. Bit Numer Math 55, 319–340 (2015). https://doi.org/10.1007/s10543-014-0505-1
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DOI: https://doi.org/10.1007/s10543-014-0505-1