Skip to main content
SpringerLink
Log in

Finite-difference method for the stabilization of the solution of the transport equation for an unstable difference scheme

  • Numerical Methods
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We present explicit three-layer difference schemes for the transport equation with the use of adaptive artificial viscosity. These schemes have the third-order approximation with respect to time and the first-order approximation with respect to space for the unstable case of forward differences. We compare these schemes with their known analogs on a series of standard tests in various norms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fedorenko, R.P., Application of High-Accuracy Finite-Difference Schemes to the Numerical Solution of Hyperbolic Equations, Zh. Vychisl. Mat. Mat. Fiz., 1962, vol. 2, no. 6, pp. 1122–1128.

    MathSciNet  Google Scholar 

  2. Babenko, K.I. and Voskresenskii, G.P., Numerical Method for the Computation of the Supersonic Flow of Bodies in Space, Zh. Vychisl. Mat. Mat. Fiz., 1961, vol. 1, no. 6, pp. 1051–1060.

    Google Scholar 

  3. Richtmyer, R.D. and Morton, K.W., Difference Methods for Initial-Value Problems, New York–London–Sydney: Interscience Publ. John Wiley & Sons, 1967. Translated under the title Raznostnye metody resheniya kraevykh zadach, Moscow, 1972.

    MATH  Google Scholar 

  4. Popov, I.V. and Fryazinov, I.V., Metod adaptivnoi iskusstvennoi vyazkosti chislennogo resheniya uravnenii gazovoi dinamiki (Method of Adaptive Artificial Viscosity for Numerical Solution of Equations of Gas Dynamics), Moscow, 2015.

    Google Scholar 

  5. Friedrichs, K.O. and Hyers, D.H., Symmetric Hyperbolic Linear Differential Equations, Commun. Pure Appl. Math., 1954, vol. 7, no. 2, pp. 345–392.

    Article  MathSciNet  MATH  Google Scholar 

  6. Kalitkin, N.N., Chislennye metody (Numerical Methods), St. Petersburg, 2011.

    Google Scholar 

  7. Bakhvalov, N.S., Zhidkov, N.P., and Kobel’kov, G.M., Chislennye metody (Numerical Methods), Moscow: Nauka, 1987.

    MATH  Google Scholar 

  8. Popov, I.V. and Timofeeva, Yu.E., Construction of a Finite-Difference Scheme of Higher Approximation Order for the Transport Equation with the Use of Adaptive Artificial Viscosity, Preprint KIAM RAS, Moscow, 2015, no.39.

    Google Scholar 

  9. Galanin, M.P. and Elenina, T.G., Testing Finite-Difference Schemes for Linear Transport Equation, Preprint KIAM RAS, Moscow, 1999, no.40.

  10. Galanin, M.P. and Elenina, T.G., Comparative Analysis of Finite-Difference Schemes for Linear Transport Equation, Preprint KIAM RAS, Moscow, 1998, no. 52.

Download references

Author information

Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Moscow, Russia

    I. V. Popov

  2. National Research Nuclear University MEPhI, Moscow, Russia

    I. V. Popov

Authors
  1. I. V. Popov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. V. Popov.

Additional information

Original Russian Text © I.V. Popov, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 7, pp. 990–1000.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Popov, I.V. Finite-difference method for the stabilization of the solution of the transport equation for an unstable difference scheme. Diff Equat 52, 951–961 (2016). https://doi.org/10.1134/S0012266116070132

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266116070132

Search

Navigation