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ISSN 2542-1905 (Online)

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Language: 
Russian
Heading: 
Modeling of Global Processes. Nonlinear Dynamics and Humanities.
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-003105
EDN: 
OXPRAL

High order accuracy scheme for modeling the dynamics of predator and prey in heterogeneous environment

Autors: 
Nguyen Buu Hoang, Southern Federal University
Tsybulin Vyacheslav Georgievich, Southern Federal University
Abstract: 

The aim of this work is to develop a compact finite-difference approach for modeling the dynamics of predator and prey based on reaction-diffusion-advection equations with variable coefficients.

Methods. To discretize a spatially inhomogeneous problem with nonlinear terms of taxis and local interaction, the balance method is used. Species densities are determined on the main grid whereas fluxes are computed at the nodes of the staggered grid. Integration over time is carried out using the high-order Runge-Kutta method.

Results. For the case of one-dimensional annular interval, the finite-difference scheme on the three-point stencil has been constructed that makes it possible to increase the order of accuracy compared to the standard second-order approximation scheme. The results of computational experiment are presented and comparison of schemes for stationary and non-stationary solutions is carried out. We conduct the calculation of accuracy order basing on the Aitken process for sequences of spatial grids. The calculated values of the effective order accuracy for the proposed scheme were greater than the standard two: for the diffusion problem, values of at least four were obtained. Decrease was obtained when directional migration was taken into account. This conclusion was also confirmed for non-stationary oscillatory regimes.

Conclusion. The results demonstrate the effectiveness of the derived scheme for dynamics of predator and prey system in a heterogeneous environment.

Key words: 
compact schemes
heterogeneous environment
predator and prey systems
Acknowledgments: 
The work was carried out at the Southern Federal University with the support of the Russian Science Foundation, grant No. 23-21-00221
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Received: 
26.01.2024
Accepted: 
14.02.2024
Available online: 
05.04.2024
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