Differential-Difference Method for the Nonlinear Cross-Systems with Absorption Function

In the article describes the methods of numerical simulation of mutual reaction-diffusion systems with double nonlinearity in multicomponent media, development of software packages. To obtain estimates of the free boundary for systems of reaction-diffusion with double nonlinearity. Development of numerical schemes of algorithms and software complexes for these problems in the multidimensional case. To investigate the properties of the finite velocity of perturbation propagation and spatial localization for a nonlinear model of polytropic filtration with double nonlinearity. To investigate the asymptotics of self-similar polytropic filtration systems in two-component media with a source. The object of research is the qualitative properties of solutions of polytropical filtration systems in a two-component medium with non-local boundary conditions. In the article uses the nonlinear splitting algorithm, the method of reference equations, the method of comparing solutions, iterative numerical methods, methods of variable directions and runs.