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 Matem. Mod., 2013, Volume 25, Number 5, Pages 55–66 (Mi mm3362)

Bicompact scheme for linear inhomogeneous transport equation

E. N. Aristovaab, D. F. Baydina, B. V. Rogovab

a Keldysh Institute of Applied Mathematics RAS
b Moscow Institute of Physics and Technology

Abstract: Generalization of bicompact finite-difference schemes, constructed for homogeneous linear transport equation, has been carried out in the case of inhomogeneous transport equation. This equation describes transport of particles or radiation in media. Bicompact scheme is constructed by means of method of lines for initial unknown function and additional unknown mesh function defined as the integral average of decision function over space cells. Comparison of the method calculation results with the conservative-characteristic method results has been done. The last method might be assigned to bicompact schemes too although it is based on the idea of true distribution of coming fluxes over cell edges.

Keywords: transport equation, finite-difference schemes, bicompact schemes, conservative schemes, Runge–Kutta methods, redistribution of fluxes.

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English version:
Mathematical Models and Computer Simulations, 2013, 5:6, 586–594

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Citation: E. N. Aristova, D. F. Baydin, B. V. Rogov, “Bicompact scheme for linear inhomogeneous transport equation”, Matem. Mod., 25:5 (2013), 55–66; Math. Models Comput. Simul., 5:6 (2013), 586–594

Citation in format AMSBIB
\Bibitem{AriBayRog13} \by E.~N.~Aristova, D.~F.~Baydin, B.~V.~Rogov \paper Bicompact scheme for linear inhomogeneous transport equation \jour Matem. Mod. \yr 2013 \vol 25 \issue 5 \pages 55--66 \mathnet{http://mi.mathnet.ru/mm3362} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3114903} \transl \jour Math. Models Comput. Simul. \yr 2013 \vol 5 \issue 6 \pages 586--594 \crossref{https://doi.org/10.1134/S2070048213060033} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925292329} 

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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. 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
2. 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
3. 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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