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Matem. Mod., 2020, Volume 32, Number 3, Pages 3–18 (Mi mm4160)  

This article is cited in 3 scientific papers (total in 3 papers)

Hermite characteristic scheme for linear inhomogeneous transport equation

E. N. Aristovaa, G. I. Ovcharovb

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

Abstract: The interpolation-characteristic scheme for the numerical solution of the inhomogeneous transport equation is constructed. The scheme is based on Hermite interpolation to reconstruction the value of unknown function at the point of intersection of the backward characteristic with the cell edges. Hermite interpolation to regeneration the values of the function uses not only the nodal values of the function, but also values of its derivative. Unlike previous works, also based on Hermitian interpolation, the differential continuation of the transport equation is not used to transfer information about the derivatives to the next layer. The relationship between the integral means, nodal values and derivatives according to the Euler–Maclaurin formula is used. The third-order convergence of the difference scheme for smooth solutions is shown. The dissipative and dispersion properties of the scheme are considered on numerical examples of solutions with decreasing smoothness.

Keywords: advection equation, interpolation-characteristic method, Hermite interpolation, Euler–Maclaurin formula.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00857_а


DOI: https://doi.org/10.20948/mm-2020-03-01

Full text: PDF file (842 kB)
References: PDF file   HTML file

Received: 01.07.2019
Revised: 01.07.2019
Accepted:09.09.2019

Citation: E. N. Aristova, G. I. Ovcharov, “Hermite characteristic scheme for linear inhomogeneous transport equation”, Matem. Mod., 32:3 (2020), 3–18

Citation in format AMSBIB
\Bibitem{AriOvc20}
\by E.~N.~Aristova, G.~I.~Ovcharov
\paper Hermite characteristic scheme for linear inhomogeneous transport equation
\jour Matem. Mod.
\yr 2020
\vol 32
\issue 3
\pages 3--18
\mathnet{http://mi.mathnet.ru/mm4160}
\crossref{https://doi.org/10.20948/mm-2020-03-01}


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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. B. V. Rogov, “Bikompaktnaya interpolyatsionno-kharakteristicheskaya skhema tretego poryadka approksimatsii dlya lineinogo uravneniya perenosa”, Preprinty IPM im. M. V. Keldysha, 2020, 106, 20 pp.  mathnet  crossref
    2. E. N. Aristova, G. O. Astafurov, “O sravnenii dissipativno-dispersionnykh svoistv nekotorykh konservativnykh raznostnykh skhem”, Preprinty IPM im. M. V. Keldysha, 2020, 117, 22 pp.  mathnet  crossref
    3. E. N. Aristova, N. I. Karavaeva, “Konservativnaya monotonizatsiya varianta CIP skhemy dlya resheniya uravneniya perenosa”, Preprinty IPM im. M. V. Keldysha, 2020, 121, 16 pp.  mathnet  crossref  elib
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