Numerical solution to the problem of cross diffusion with nonlocal boundary conditions

Аннотация

In this paper, we study the asymptotic behavior of self-similar solutions of a nonlinear cross-diffusion system coupled in the nonlocal boundary conditions. On the basis of selfsimilar analysis the main term of the asymptotics of self-similar solutions is obtained. A numerical scheme is constructed based on the finite difference method. For this, equations are approximated with the second order of accuracy in spatial coordinates and with the first order in t.