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Matem. Mod., 2011, Volume 23, Number 6, Pages 98–110 (Mi mm3122)  

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

Bibliographic databases:

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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\by B.~V.~Rogov, M.~N.~Mikhailovskaya
\paper The monotonic bicompact schemes for a linear transfer equation
\jour Matem. Mod.
\yr 2011
\vol 23
\issue 6
\pages 98--110
\mathnet{http://mi.mathnet.ru/mm3122}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2866558}
\elib{http://elibrary.ru/item.asp?id=21276628}
\transl
\jour Math. Models Comput. Simul.
\yr 2012
\vol 4
\issue 1
\pages 92--100
\crossref{https://doi.org/10.1134/S2070048212010103}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84860588056}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet
    2. B. V. Rogov, M. N. Mikhailovskaya, “Monotone high-precision compact scheme for quasilinear hyperbolic equations”, Math. Models Comput. Simul., 4:4 (2012), 375–384  mathnet  crossref  mathscinet
    3. M. N. Mikhailovskaya, B. V. Rogov, “Monotone compact running schemes for systems of hyperbolic equations”, Comput. Math. Math. Phys., 52:4 (2012), 672–695  mathnet  crossref  mathscinet  isi  elib  elib
    4. 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  mathnet  crossref  mathscinet
    5. 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  mathnet  crossref  mathscinet
    6. 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  mathnet  crossref  mathscinet  elib
    7. 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  mathnet  crossref  crossref  isi  elib  elib
    8. 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  mathnet  crossref  mathscinet  elib
    9. 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  mathnet  crossref  elib
    10. 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  mathnet  crossref  elib
    11. 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  mathnet  crossref  crossref  isi  elib
    12. E. N. Aristova, N. I. Karavaeva, “Bikompaktnye skhemy vysokogo poryadka approksimatsii dlya uravnenii kvazidiffuzii”, Preprinty IPM im. M. V. Keldysha, 2018, 045, 28 pp.  mathnet  crossref  elib
    13. 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  mathnet  crossref  crossref  isi  elib
    14. 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.  mathnet  crossref  elib
    15. 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  crossref  isi
    16. V. A. Gordin, “Kompaktnye raznostnye skhemy dlya approksimatsii differentsialnykh sootnoshenii”, Matem. modelirovanie, 31:7 (2019), 58–74  mathnet  crossref  elib
    17. 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  mathnet  crossref  elib
    18. 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  mathnet  crossref  elib
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