USSR Computational Mathematics and Mathematical Physics
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition in boundary layers for singularly perturbed problems
Applied Numerical Mathematics - Auckl numerical ordinary differential equations (ANODE 98 workshop)
Monotone iterative algorithms for a nonlinear singularly perturbed parabolic problem
Journal of Computational and Applied Mathematics
A block monotone domain decomposition algorithm for a semilinear convection-diffusion problem
Journal of Computational and Applied Mathematics
Nonstationary monotone iterative methods for nonlinear partial differential equations
Journal of Computational and Applied Mathematics
Monotone Schwarz iterates for a semilinear parabolic convection-diffusion problem
Journal of Computational and Applied Mathematics
Advances in Computational Mathematics
Uniform convergence of a monotone iterative method for a nonlinear reaction-diffusion problem
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
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This paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed reaction-diffusion problem. Firstly, the monotone method (known as the method of lower and upper solutions) is applied to computing a nonlinear difference scheme obtained after discretisation of the continuous problem. 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 of the iterative process. The rate of convergence of the monotone Schwarz method is estimated. Numerical experiments are presented.