2024 , Volume 29, № 5, p.30-42

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.