Monotone algorithms for solving nonlinear monotone difference schemes of parabolic type in the canonical form

Abstract

This paper deals with monotone iterative algorithms for solving nonlinear monotone difference schemes of parabolic type. Firstly, the monotone method (known as the method of lower and upper solutions) is applied to computing the nonlinear monotone difference schemes in the canonical form. Secondly, a monotone domain decomposition algorithm based on a modification of the Schwarz alternating method is constructed. This monotone algorithm solves only linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear monotone difference schemes. Numerical experiments are presented.