A Block Monotone Domain Decomposition Algorithm for a Nonlinear Singularly Perturbed Parabolic Problem

Abstract

This paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed parabolic problem. A block monotone domain decomposition algorithm based on a Schwarz alternating method and on a block iterative scheme is constructed. This monotone algorithm solves only linear discrete systems at each time level and converges monotonically to the exact solution of the nonlinear problem. The rate of convergence of the block monotone domain decomposition algorithm is estimated. Numerical experiments are presented.