This article is cited in 2 scientific papers (total in 2 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
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.
singularly perturbed problems, Helmholz equation, error estimation, Richardson method.
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Mathematical Models and Computer Simulations, 2016, 8:4, 341–347
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
Citation in format AMSBIB
\by A.~A.~Belov, N.~N.~Kalitkin
\paper Numerical simulations of boundary layer problems
\jour Matem. Mod.
\jour Math. Models Comput. Simul.
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