Monotone iterative ADI method for solving coupled systems of nonlinear parabolic equations

The paper deals with numerical solution of coupled systems of nonlinear parabolic equations based on a nonlinear ADI scheme. The convergence of the nonlinear ADI scheme to the continuous solution is proved. A monotone iterative ADI method is constructed. The existence and uniqueness of a solution of the nonlinear ADI scheme are established. An analysis of convergence of the monotone iterative ADI method to the solution of the nonlinear ADI scheme on the whole time interval is given. Numerical experiments are presented.