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This article is cited in 18 scientific papers (total in 18 papers)
The monotonic bicompact schemes for a linear transfer equation
B. V. Rogova, M. N. Mikhailovskayab
a Keldysh Institute of Applied Mathematics of RAS, Moscow
b Moscow Institute of Physics and Technology, State University
Abstract:
It is shown that previously proposed by the authors bicompact difference scheme for a linear transport equation, which has the fourth-order approximation in spatial coordinate on a two-point stencil and the first order approximation in time, is monotonic. This implicit scheme is absolutely stable and can be solved by explicit formulas of the running calculation method. On the basis of this scheme the monotone nonlinear homogeneous difference scheme of high (third for smooth solutions) order accuracy in time is constructed. Calculations of the test problems with discontinuous solutions showed a significant advantage in the accuracy of the proposed scheme over known nonoscillatory schemes of high-order approximation.
Keywords:
transport equation, bicompact difference schemes, monotonicity
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English version:
Mathematical Models and Computer Simulations, 2012, 4:1, 92–100
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UDC:
519.6
Received: 14.12.2010
Citation:
B. V. Rogov, M. N. Mikhailovskaya, “The monotonic bicompact schemes for a linear transfer equation”, Matem. Mod., 23:6 (2011), 98–110; Math. Models Comput. Simul., 4:1 (2012), 92–100
Citation in format AMSBIB
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\jour Matem. Mod.
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\vol 23
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\pages 98--110
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\jour Math. Models Comput. Simul.
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\vol 4
\issue 1
\pages 92--100
\crossref{https://doi.org/10.1134/S2070048212010103}
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http://mi.mathnet.ru/eng/mm3122 http://mi.mathnet.ru/eng/mm/v23/i6/p98
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This publication is cited in the following articles:
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M. N. Mikhailovskaya, B. V. Rogov, “The bicompact monotonic schemes for a multidimensional linear transport equation”, Math. Models Comput. Simul., 4:3 (2012), 355–362
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B. V. Rogov, M. N. Mikhailovskaya, “Monotone high-precision compact scheme for quasilinear hyperbolic equations”, Math. Models Comput. Simul., 4:4 (2012), 375–384
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M. N. Mikhailovskaya, B. V. Rogov, “Monotone compact running schemes for systems of hyperbolic equations”, Comput. Math. Math. Phys., 52:4 (2012), 672–695
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E. N. Aristova, B. V. Rogov, “About implementation of boundary conditions in the bicompact schemes for a linear transport equation”, Math. Models Comput. Simul., 5:3 (2013), 199–207
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E. N. Aristova, D. F. Baydin, B. V. Rogov, “Bicompact scheme for linear inhomogeneous transport equation”, Math. Models Comput. Simul., 5:6 (2013), 586–594
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E. N. Aristova, “Bicompact scheme for linear inhomogeneous transport equation in a case of a big optical width”, Math. Models Comput. Simul., 6:3 (2014), 227–238
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E. N. Aristova, S. V. Martynenko, “Bicompact Rogov schemes for the multidimensional inhomogeneous linear transport equation at large optical depths”, Comput. Math. Math. Phys., 53:10 (2013), 1499–1511
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E. N. Aristova, B. V. Rogov, A. V. Chikitkin, “Monotonization of high accuracy bicompact scheme for stationary multidimensional transport equation”, Math. Models Comput. Simul., 8:2 (2016), 108–117
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V. I. Golubev, I. B. Petrov, N. I. Khokhlov, “Compact grid-characteristic schemes of higher orders for 3D linear transport equation”, Math. Models Comput. Simul., 8:5 (2016), 577–584
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E. N. Aristova, M. I. Stoynov, “Bicompact schemes of solving an stationary transport equation by quasi–diffusion method”, Math. Models Comput. Simul., 8:6 (2016), 615–624
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E. N. Aristova, B. V. Rogov, A. V. Chikitkin, “Optimal monotonization of a high-order accurate bicompact scheme for the nonstationary multidimensional transport equation”, Comput. Math. Math. Phys., 56:6 (2016), 962–976
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E. N. Aristova, N. I. Karavaeva, “Bikompaktnye skhemy vysokogo poryadka approksimatsii dlya uravnenii kvazidiffuzii”, Preprinty IPM im. M. V. Keldysha, 2018, 045, 28 pp.
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A. I. Lobanov, F. Kh. Mirov, “A hybrid difference scheme under generalized approximation condition in the space of undetermined coefficients”, Comput. Math. Math. Phys., 58:8 (2018), 1270–1279
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E. N. Aristova, N. I. Karavaeva, “Realizatsiya bikompaktnoi skhemy dlya HOLO algoritmov resheniya uravneniya perenosa”, Preprinty IPM im. M. V. Keldysha, 2019, 021, 28 pp.
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Matias D.V., Vitokhin E.Yu., “A Comparison of the Finite-Difference and Finite-Volume Methods For a Numerical Solution of a Hyperbolic Thermoelasticity Problem Utilizing the Implicit and Explicit Schemes”, ZAMM-Z. Angew. Math. Mech., 99:5 (2019), UNSP e201700369
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V. A. Gordin, “Kompaktnye raznostnye skhemy dlya approksimatsii differentsialnykh sootnoshenii”, Matem. modelirovanie, 31:7 (2019), 58–74
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E. N. Aristova, N. I. Karavaeva, “Postanovka granichnykh uslovii v bikompaktnykh skhemakh dlya HOLO algoritmov resheniya uravneniya perenosa”, Matem. modelirovanie, 31:9 (2019), 3–20
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B. V. Rogov, A. V. Chikitkin, “O skhodimosti i tochnosti metoda iteriruemoi priblizhennoi faktorizatsii operatorov mnogomernykh vysokotochnykh bikompaktnykh skhem”, Matem. modelirovanie, 31:12 (2019), 119–144
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