Integrable Discretisation of the Lotka-Volterra System

Integrable Discretisation of the Lotka-Volterra System

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.

Author Details

Yang He

Yajuan Sun

Zaijiu Shang