Article information

2024 , Volume 29, ¹ 5, p.30-42

Nguyen B.H., Ha T.D., Tsybulin V.G.

Compact scheme for modelling competing dynamics of populations on a heterogeneous environment

The research is aimed to describe the numerical method for studying population models based on the reaction – diffusion – advection equations with variable coefficients. It is important to analyze the impact of directed migration towards a resource on temporal-spatial competition of species. We apply a method of lines with a staggered grid for discretizing the nonlinear problems with high order accuracy on three-point stencil in spatial coordinate. To integrate in time, a highorder Runge – Kutta method is used (ode89 in MATLAB). The scheme was tested using special problems allowing exact solutions. We carried out calculations of stationary distributions for species in a heterogeneous environment under various boundary conditions. Numerical estimates of accuracy orders were obtained using the given scheme and compared with the second order approximation analogue. We performed a computational experiment to assess the order of approximation with nonstationary regimes using the Aitken process. Our results demonstrate the effectiveness of a compact scheme for calculating the dynamics of three species competing in a heterogeneous habitat.


Keywords: compact schemes, heterogeneous environment, system of competing populations

doi: 10.25743/ICT.2024.29.5.004

Author(s):
Nguyen Buu Hoang
Position: Student
Office: Southern Federal University
Address: 344090, Russia, Rostov -na-Donu
E-mail: kng@sfedu.ru

Ha Toan Dang
PhD.
Position: Lecture
Office: Viet-Hung Industrial University
Address: Vietnam, Hanoi, Rostov -na-Donu
E-mail: toanhd.viu@gmail.com

Tsybulin Vyacheslav Georgievich
Dr. , Associate Professor
Position: Head of Chair
Office: Southern Federal University
Address: 344090, Russia, Rostov -na-Donu
E-mail: vgcibulin@sfedu.ru
SPIN-code: 7027-2045


Bibliography link:
Nguyen B.H., Ha T.D., Tsybulin V.G. Compact scheme for modelling competing dynamics of populations on a heterogeneous environment // Computational technologies. 2024. V. 29. ¹ 5. P. 30-42
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