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An Improved Difference Scheme for the Cauchy Problem in the Case of a Transport Equation

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Abstract

The Cauchy problem for the regular transport equation is considered. The Richardson technique is used to construct an improved difference scheme that converges in the maximum norm with the second order of convergence.

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REFERENCES

  1. G. I. Marchuk, Methods of Numerical Mathematics (Nauka, Moscow, 1989; Springer, New York, 1982).

  2. G. I. Marchuk and V. V. Shaidurov, Difference Methods and Their Extrapolations (Springer, New York, 1983).

    Book  MATH  Google Scholar 

  3. A. A. Samarskii, Theory of Finite Difference Schemes (Nauka, Moscow, 1989; Marcel Dekker, New York, 2001).

  4. G. I. Shishkin and L. P. Shishkina, Difference Methods for Singular Perturbation Problems, Vol. 140 of Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics (CRC, Boca Raton, FL, 2009).

  5. N. N. Kalitkin, Numerical Methods (Nauka, Moscow, 1978) [in Russian].

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  6. G. I. Shishkin, “Difference scheme for an initial–boundary value problem for a singularly perturbed transport equation,” Comput. Math. Math. Phys. 57 (11), 1789–1795 (2017).

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, 620108, Yekaterinburg, Russia

    G. I. Shishkin & L. P. Shishkina

Authors
  1. G. I. Shishkin
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  2. L. P. Shishkina
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Correspondence to G. I. Shishkin.

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The authors declare that they have no conflicts of interest.

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Translated by A. Klimontovich

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Shishkin, G.I., Shishkina, L.P. An Improved Difference Scheme for the Cauchy Problem in the Case of a Transport Equation. Comput. Math. and Math. Phys. 63, 1401–1407 (2023). https://doi.org/10.1134/S0965542523080134

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  • DOI: https://doi.org/10.1134/S0965542523080134

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