Geodesic
Variable piecewise interpolation solution of the transport equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part II, Tome 166 (2019), pp. 77-86

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In this paper, we construct a piecewise interpolation method of approximate solution of the transport equation based on the Newton interpolation polynomial of two variables. We transform the polynomial to the algebraic form with numerical coefficients; this leads us to a sequence of iterations, which improves the accuracy of the approximation. The method is implemented in software and numerical experiments ares performed. The possibility of generalizations to systems of partial differential equations and integro-differential equations is discussed.
Mots-clés : piecewise interpolation approximation, transport equation.
Keywords: Newton interpolation polynomial for a function of two variables, Cauchy problem for partial differential equations 
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     title = {Variable piecewise interpolation solution of the transport equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
     volume = {166},
     year = {2019},
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Ya. E. Romm; G. A. Dzhanunts. Variable piecewise interpolation solution of the transport equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part II, Tome 166 (2019), pp. 77-86. http://geodesic.mathdoc.fr/item/INTO_2019_166_a7/