A monotone domain decomposition algorithm for nonlinear parabolic difference schemes

Abstract

A monotone domain decomposition algorithm for a nonlinear algebraic system, which is a finite difference approximation of a nonlinear reaction-diffusion problem of parabolic type, is presented and is shown to converge monotonically either from above or from below to a solution of the system. The algorithm is based on a modification of the Schwarz alternating method and the method of upper and lower solutions. Advantages of the algorithm are that the algorithm solves only linear discrete systems at each iterative step, converges monotonically to the exact solution of the system, and is potentially parallelisable. Numerical experiments for a model problem from chemical engineering are presented.