A block monotone domain decomposition algorithm for a semilinear convection–diffusion problem

This paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed convection–diffusion problem. A block monotone domain decomposition algorithm based on a Schwarz alternating method and on block iterative scheme is constructed. This monotone algorithm solves only linear discrete systems at each iterative step of the iterative process 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.