Geodesic
Uniform convergence of monotone iterative methods for semilinear singularly perturbed problems of elliptic and parabolic types
Electronic transactions on numerical analysis, Tome 20 (2005), pp. 86-103
This paper deals with discrete monotone iterative methods for solving semilinear singularly perturbed problems of elliptic and parabolic types. The monotone iterative methods solve only linear discrete systems at each iterative step of the iterative process. Uniform convergence of the monotone iterative methods are investigated and rates of convergence are estimated. Numerical experiments complement the theoretical results.
Classification : 65M06, 65N06
Keywords: singular perturbation, reaction-diffusion problem, convection-diffusion problem, discrete monotone iterative method, uniform convergence 
@article{ETNA_2005__20__a10,
     author = {Boglaev,  Igor},
     title = {Uniform convergence of monotone iterative methods for semilinear singularly perturbed problems of elliptic and parabolic types},
     journal = {Electronic transactions on numerical analysis},
     pages = {86--103},
     year = {2005},
     volume = {20},
     zbl = {1077.65096},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2005__20__a10/}
}
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%A Boglaev,  Igor
%T Uniform convergence of monotone iterative methods for semilinear singularly perturbed problems of elliptic and parabolic types
%J Electronic transactions on numerical analysis
%D 2005
%P 86-103
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%U http://geodesic.mathdoc.fr/item/ETNA_2005__20__a10/
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%F ETNA_2005__20__a10
Boglaev,  Igor. Uniform convergence of monotone iterative methods for semilinear singularly perturbed problems of elliptic and parabolic types. Electronic transactions on numerical analysis, Tome 20 (2005), pp. 86-103. http://geodesic.mathdoc.fr/item/ETNA_2005__20__a10/