Skip to main content
Log in

Grid methods for a boundary layer problem

  • Proceedings of the XV All-Russian Seminar “Physics and the Application of Microwaves” (Waves 2015) Named after Prof. A.P. Sukhorukov
  • Published:
Bulletin of the Russian Academy of Sciences: Physics Aims and scope

Abstract

Up-to-date finite-difference schemes are shown to allow us to solve boundary layer problems effectively provided the mesh is chosen appropriately. A procedure of obtaining an a posteriori asymptotically precise error estimation is proposed. A superfast algorithm applicable to a wide range of problems is described, and a semi-uniform rectangular grid that resolves all parts of the solution is proposed.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Toth, C.D., O’Rourke, R., and Goodman, J.E., Handbook of Discrete and Computational Geometry, London: Chapman & Hall/CRC, 2004.

    Google Scholar 

  2. Bakhvalov, N.S., Zh. Vychisl. Mat. Mat. Fiz., 1969, vol. 9, no. 4, pp. 841–859.

    MATH  Google Scholar 

  3. Shishkin, G.I., Zh. Vychisl. Mat. Mat. Fiz., 1987, vol. 27, no. 9, pp. 1360–1372.

    MATH  MathSciNet  Google Scholar 

  4. Kalitkin, N.N., Al’shin, A.B., Al’shina, E.A., and Rogov, B.V., Vychisleniya na kvaziravnomernykh setkakh (Calculations at Semi-uniform Grids), Moscow: Fizmatlit, 2005.

    Google Scholar 

  5. Ryaben’kii, V.S. and Fillipov, A.F., Ob ustoichivosti raznostnykh uravnenii (On Difference Equations Stability), Moscow: Gos. Izd. Tekhn.-Teoret. Lit., 1956.

    Google Scholar 

  6. Kalitkin, N.N. and Koryakin, P.V., Chislennye metody (Numerical Methods), book 2: Metody matematicheskoi fiziki (Methods of Mathematical Physics), Moscow: Akademiya, 2013.

    Google Scholar 

  7. Samarskii, A.A. and Gulin, A.V., Chislennye metody (Numerical Methods), Moscow: Nauka, 1989.

    Google Scholar 

  8. Kalitkin, N.N., Dokl. Akad. Nauk, 2005, vol. 402, no. 4, pp. 467–471.

    MATH  MathSciNet  Google Scholar 

  9. Boltnev, A.A., Kalitkin, N.N., and Kacher, O.A., Dokl. Akad. Nauk, 2005, vol. 404, no. 2, pp. 177–180.

    MathSciNet  Google Scholar 

  10. Kalitkin, N.N. and Belov, A.A., Dokl. Akad. Nauk, 2013, vol. 452, no. 3, pp. 261–265.

    MathSciNet  Google Scholar 

  11. Belov, A.A and Kalitkin, N.N., Mat. Model., 2014, vol. 26, no. 9, pp. 47–64.

    Google Scholar 

  12. Belov, A.A. and Kalitkin, N.N., Evolutional factorization and superfast calculation for establishing, Preprint of Keldysh Institute of Applied Mathematics, Moscow, 2013, no. 69.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Belov.

Additional information

Original Russian Text © A.A. Belov, N.N. Kalitkin, 2015, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2015, Vol. 79, No. 12, pp. 1655–1659.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Belov, A.A., Kalitkin, N.N. Grid methods for a boundary layer problem. Bull. Russ. Acad. Sci. Phys. 79, 1448–1452 (2015). https://doi.org/10.3103/S1062873815120072

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1062873815120072

Keywords

Navigation