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Variable Piecewise Interpolation Solution of the Transport Equation

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Abstract

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 are performed. The possibility of generalizations to systems of partial differential equations and integro-differential equations is discussed.

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Authors and Affiliations

  1. A. P. Chekhov Taganrog Institute (Branch) of the Rostov State Economic University, Taganrog, Russia

    Ya. E. Romm & G. A. Dzhanunts

Authors
  1. Ya. E. Romm
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  2. G. A. Dzhanunts
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Correspondence to Ya. E. Romm.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 166, Proceedings of the IV International Scientific Conference “Actual Problems of Applied Mathematics,” Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part II, 2019.

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Romm, Y.E., Dzhanunts, G.A. Variable Piecewise Interpolation Solution of the Transport Equation. J Math Sci 260, 230–240 (2022). https://doi.org/10.1007/s10958-022-05687-1

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  • DOI: https://doi.org/10.1007/s10958-022-05687-1

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