Monotone iterates for solving coupled systems of nonlinear parabolic equations

This paper deals with numerical solutions of coupled nonlinear parabolic equations. Using the method of upper and lower solutions, monotone sequences are constructed for difference schemes which approximate coupled systems of nonlinear parabolic equations. This monotone convergence leads to existence-uniqueness theorems. An analysis of convergence rates of the monotone iterative method is given. A monotone domain decomposition algorithm which combines the monotone approach and an iterative domain decomposition method based on the Schwarz alternating is proposed. A convergence analysis of the monotone domain decomposition algorithm is presented. An application to a gas-liquid interaction model is given.