Skip to main content
SpringerLink
Log in

Quadratures with Superpower Convergence

  • Published:
Bulletin of the Russian Academy of Sciences: Physics Aims and scope

Abstract

It is suggested that changing the variables of integration in quadrature calculations greatly improves the accuracy of the rule of means. The law of convergence becomes a superpower for infinitely smooth integrand functions. Its rate is much faster than that of a power law and is close to exponential. Power law convergence is achieved with the maximum attainable order of accuracy for integrand functions of limited smoothness.

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

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

REFERENCES

  1. Kalitkin, N.N. and Al’shina, E.A., Chislennye metody (Numerical Methods), vol. 1: Chislennyi analiz (Numerical Analysis), Moscow: Akademiya, 2013.

  2. Kalitkin, N.N., Al’shin, A.B., Al’shina, E.A., and Rogov, B.V., Vychisleniya na kvaziravnomernykh setkakh (Computations with Quasi-Uniform Grids), Moscow: Fizmatlit, 2005.

  3. Trefethen, L.N. and Weideman, J.A.C., SIAM Rev. E, 2014, vol. 56, no. 3, p. 385.

    Google Scholar 

  4. Kalitkin, N.N. and Kolganov, S.A., Dokl. Math., 2017, vol. 95, no. 2, p. 157.

    Article  MathSciNet  Google Scholar 

  5. Kalitkin, N.N. and Kolganov, S.A., Math. Models Comput. Simul., 2018, vol. 10, no. 4, p. 472.

    Article  MathSciNet  Google Scholar 

  6. Sag, T.W. and Szekeres, G., Math. Comput., 1964, vol. 18, p. 245.

    Article  Google Scholar 

  7. Sidi, A., Int. Ser. Numer. Math., 1993, vol. 112, p. 359.

    Google Scholar 

  8. Iri, M., Moriguti, S., and Takasawa, Y., J. Comput. Appl. Math., 1987, vol. 17, p. 3.

    Article  MathSciNet  Google Scholar 

  9. Mori, M., Publ. Res. Inst. Math. Sci. Kyoto Univ., 1978, vol. 14, p. 713.

    Article  Google Scholar 

  10. Belov, A.A., Kalitkin, N.N., and Khokhlachev, V.S., Preprint of the Keldysh Appl. Math. Inst., Moscow, 2020, no. 75.

  11. Khokhlachev, V.S., Belov, A.A., and Kalitkin, N.N., Izv. Akad. Nauk, Ser. Fiz., 2021, vol. 85, no. 2, p. 282.

    Google Scholar 

Download references

Funding

This work was supported by the Russian Science Foundation, project no. 22-71-00028.

Author information

Authors and Affiliations

  1. Faculty of Physics, Moscow State University, 119991, Moscow, Russia

    M. A. Tintul, V. S. Khokhlachev & A. A. Belov

  2. Peoples’ Friendship University of Russia (RUDN University), 117198, Moscow, Russia

    A. A. Belov

Authors
  1. M. A. Tintul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. S. Khokhlachev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. A. Belov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Tintul.

Ethics declarations

The authors declare they have no conflicts of interest.

Additional information

Translated by O. Ponomareva

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tintul, M.A., Khokhlachev, V.S. & Belov, A.A. Quadratures with Superpower Convergence. Bull. Russ. Acad. Sci. Phys. 86, 1350–1354 (2022). https://doi.org/10.3103/S1062873822110302

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1062873822110302

Search

Navigation