Monotone iterative algorithms for a nonlinear singularly perturbed parabolic problem

Authors:
Igor Boglaev
Affiliations:
Institute of Fundamental Sciences, Massey University, Private Bag 11-222, Palmerston North, New Zealand
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

Citing 3
Cited 3

Sufficient conditions for uniform convergence on layer-adapted grids

Computing
Iterative solution of nonlinear equations in several variables

Iterative solution of nonlinear equations in several variables
On monotone iterative methods for a nonlinear singularly perturbed reaction-diffusion problem

Journal of Computational and Applied Mathematics

Monotone Schwarz iterates for a semilinear parabolic convection-diffusion problem

Journal of Computational and Applied Mathematics
Uniform convergent monotone iterates for semilinear singularly perturbed parabolic problems

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Parallel monotone domain decomposition algorithms for nonlinear singularly perturbed reaction-diffusion problems of parabolic type

Neural, Parallel & Scientific Computations

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Abstract

This paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed parabolic 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 domain decomposition algorithm is estimated. Numerical experiments are presented.