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Uniqueness of a high-order accurate bicompact scheme for quasilinear hyperbolic equations

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Abstract

The possibility of constructing new third- and fourth-order accurate differential-difference bicompact schemes is explored. The schemes are constructed for the one-dimensional quasilinear advection equation on a symmetric three-point spatial stencil. It is proved that this family of schemes consists of a single fourth-order accurate bicompact scheme. The result is extended to the case of an asymmetric three-point stencil.

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References

  1. A. I. Tolstykh, Compact Difference Schemes and Their Application to Aerohydrodynamic Problems (Nauka, Moscow, 1990) [in Russian].

    Google Scholar 

  2. S. Zhang, S. Jiang, and C.-W. Shu, “Development of nonlinear weighted compact schemes with increasingly higher order accuracy,” J. Comput. Phys. 227, 7294–7321 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  3. S. K. Lele, “Compact finite difference schemes with spectral-like resolution,” J. Comput. Phys. 103(1), 16–42 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  4. M. N. Mikhailovskaya and B. V. Rogov, “Monotone compact running schemes for systems of hyperbolic equations,” Comput. Math. Math. Phys. 52, 578–600 (2012).

    Article  Google Scholar 

  5. B. V. Rogov, “High-order accurate monotone compact running scheme for multidimensional hyperbolic equations,” Comput. Math. Math. Phys. 53, 205–214 (2013).

    Article  Google Scholar 

  6. B. V. Rogov, “Monotone bicompact scheme for quasilinear hyperbolic equations,” Dokl. Math. 86, 715–719 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  7. E. N. Aristova and B. V. Rogov, “Implementation of boundary conditions in bicompact schemes for the linear transport equation,” Mat. Model. 24(10), 3–14 (2012).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

    M. D. Bragin & B. V. Rogov

  2. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

    B. V. Rogov

Authors
  1. M. D. Bragin
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  2. B. V. Rogov
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Correspondence to M. D. Bragin.

Additional information

Original Russian Text © M.D. Bragin, B.V. Rogov, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 5, pp. 815–820.

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Bragin, M.D., Rogov, B.V. Uniqueness of a high-order accurate bicompact scheme for quasilinear hyperbolic equations. Comput. Math. and Math. Phys. 54, 831–836 (2014). https://doi.org/10.1134/S0965542514050066

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  • DOI: https://doi.org/10.1134/S0965542514050066

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