Numerical solution of nonlinear parabolic systems by block monotone methods

Abstract

This paper deals with numerical methods for solving systems of nonlinear parabolic problems. Block monotone iterative methods, based on the Jacobi and Gauss–Seidel methods, are in use for solving nonlinear difference schemes which approximate the systems of nonlinear parabolic problems. In the view of the method of upper and lower solutions, two monotone upper and lower sequences of solutions are constructed, where the monotone property ensures the theorem on existence and uniqueness of solutions. Constructions of initial upper and lower solutions are discussed. Numerical experiments are presented.