TY - JOUR
T1 - Integrable Discretisation of the Lotka-Volterra System
AU - He , Yang
AU - Sun , Yajuan
AU - Shang , Zaijiu
JO - Journal of Computational Mathematics
VL - 5
SP - 468
EP - 494
PY - 2015
DA - 2015/10
SN - 33
DO - http://doi.org/10.4208/jcm.1504-m4543
UR - https://global-sci.org/intro/article_detail/jcm/9855.html
KW - Integrable Lotka-Volterra system, Hirota's integrable discretisation, Backward
error analysis, Modified differential equation.
AB - <p style="text-align: justify;">In this paper, we apply Hirota&#39;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.</p>