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This article is cited in 3 scientific papers (total in 3 papers)
Numerical simulations of boundary layer problems
A. A. Belovab, N. N. Kalitkinb a Lomonosov Moscow State University, Faculty of Physics, Moscow
b Keldysh Institute of Applied Mathematics of RAS, Moscow
Abstract:
At the interface between two media there often appear boundary layers. Singularly perturbed Helmholz equation is typical example. Up-to-date finite difference methods are shown to be capable of effective solving of such problems. Convergence verification procedure is proposed that does not require a priori estimations construction. A superfast algorithm that provides a posteriori asymptotically precise error estimation is described and semi-uniform rectangular grid that resolves all parts of solution is proposed. The algorithm proposed makes it possible to achieve good precisions on moderate grids with number of points $N\sim 200$ in each direction. This algorithm is realized as a program in Matlab environment.
Keywords:
singularly perturbed problems, Helmholz equation, error estimation, Richardson method.
Received: 05.11.2014
Citation:
A. A. Belov, N. N. Kalitkin, “Numerical simulations of boundary layer problems”, Matem. Mod., 27:11 (2015), 47–55; Math. Models Comput. Simul., 8:4 (2016), 341–347
Linking options:
https://www.mathnet.ru/eng/mm3667 https://www.mathnet.ru/eng/mm/v27/i11/p47
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Abstract page: | 450 | Full-text PDF : | 182 | References: | 52 | First page: | 20 |
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