Year: 2015
Author: Yang He, Yajuan Sun, Zaijiu Shang
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 5 : pp. 468–494
Abstract
In this paper, we apply Hirota's discretisation to a three-dimensional integrable Lotka-Volterra system. By analyzing the three-dimensional modified equation of the resulting numerical method, we show that it is volume-preserving, and has two independent first integrals. Moreover, it can be formally reduced to a system in one dimension via a volume-preserving transformation. If the given initial value is located in the positive octant, we prove that the numerical solution is confined to a one-dimensional connected and compact space which is diffeomorphic to a circle.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1504-m4543
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 5 : pp. 468–494
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Integrable Lotka-Volterra system Hirota's integrable discretisation Backward error analysis Modified differential equation.