Geometric Numerical Integration in Ecological Modelling

Fasma Diele and Carmela Marangi
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Fasma Diele: Istituto per Applicazioni del Calcolo M.Picone, via Amendola 122/D, 70126 Bari, Italy
Carmela Marangi: Istituto per Applicazioni del Calcolo M.Picone, via Amendola 122/D, 70126 Bari, Italy

Mathematics, 2019, vol. 8, issue 1, 1-30

Abstract: A major neglected weakness of many ecological models is the numerical method used to solve the governing systems of differential equations. Indeed, the discrete dynamics described by numerical integrators can provide spurious solution of the corresponding continuous model. The approach represented by the geometric numerical integration, by preserving qualitative properties of the solution, leads to improved numerical behaviour expecially in the long-time integration. Positivity of the phase space, Poisson structure of the flows, conservation of invariants that characterize the continuous ecological models are some of the qualitative characteristics well reproduced by geometric numerical integrators. In this paper we review the benefits induced by the use of geometric numerical integrators for some ecological differential models.

Keywords: geometric numerical integration; positive methods; Poisson integrators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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