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Matematicheskoe modelirovanie, 1998, Volume 10, Number 1, Pages 117–125 (Mi mm1243)  

This article is cited in 2 scientific papers (total in 2 papers)

Computational methods and algorithms

The method of constructing of block-triangular difference schemes for selfadjoint form of the transport equation

V. E. Troshchiev

Troitsk Institute for Innovation and Fusion Research
Full-text PDF (790 kB) Citations (2)
Abstract: The method is proposed for construction of difference schemes for the 2nd order linear transport equation: \[ M\varphi(\vec{r},\vec{\Omega})\equiv\operatorname{div}[ \vec\Omega\frac1{\sigma(\vec{r})}(-\vec\Omega\nabla\varphi +\frac1{4\pi}Q(\vec{r},\vec{\Omega}))] +\sigma(\vec{r})\cdot\varphi=\frac1{4\pi}Q(\vec{r},\vec{\Omega})\tag{1} \] under the assumption that $Q(\vec{r},\vec{\Omega})$ is a given function (simple iteration). Equation (1) is one among selfadjoint forms equivalent to the transport equation of the 1st order: \[ L\varphi(\vec{r},\vec{\Omega})\equiv\vec{\Omega}\cdot\nabla\varphi +\sigma(\vec{r})\cdot\varphi=\frac1{4\pi}Q(\vec{r},\vec{\Omega}). \tag{2} \] The problem of the equation (1) is stated in a convex body $G$ and is a boundary problem in contrast to the equation (2), for which Cauchy problem is stated. The novelty of the method is that some properties of the problem (1) are indicated, and these properties make it possible to build finitedifference and finite-elements schemes with block-triangular matrices for boundary value for the system of discrete equations.
Received: 12.05.1997
Bibliographic databases:
Language: Russian
Citation: V. E. Troshchiev, “The method of constructing of block-triangular difference schemes for selfadjoint form of the transport equation”, Matem. Mod., 10:1 (1998), 117–125
Citation in format AMSBIB
\Bibitem{Tro98}
\by V.~E.~Troshchiev
\paper The method of constructing of block-triangular difference schemes for selfadjoint form of the transport equation
\jour Matem. Mod.
\yr 1998
\vol 10
\issue 1
\pages 117--125
\mathnet{http://mi.mathnet.ru/mm1243}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1758781}
\zmath{https://zbmath.org/?q=an:1189.82111}
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  • https://www.mathnet.ru/eng/mm/v10/i1/p117
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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