Solving parabolic problems with different time steps in different regions in space based on domain decomposition methods (Q1294615)

The paper deals with the numerical solution of systems of nonlinear parabolic equations having the form \[ u_t+ f(t, x, y,u,u_x, u_y)= [D_1(t, x,y,u) u_x]_x+ [D_2(t, x,y,u) u_y]_y, \] equipped with some initial conditions and boundary conditions of mixed type. It is supposed that the matrices \(D_1\), \(D_2\) are positive definite. After describing the proposed algorithms, the author presents a number of numerical examples.