Skip to main content
SpringerLink
Log in

On calculation of integrals over spherical domains

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We construct cubature formulas for the computation of integrals over spherical domains containing less nodes as compared with known ones.

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. S. L. Sobolev, “On formulas of mechanical cubatures on the surface of a sphere,” Sib. Mat. Zh., 3, No. 5, 769–791 (1962).

    MATH  MathSciNet  Google Scholar 

  2. G. N. Salikhov, Cubature Formulas for Multidimensional Spheres [in Russian], Fan, Tashkent (1985).

    MATH  Google Scholar 

  3. V. I. Lebedev, “On quadratures on a sphere with highest algebraic degree of accuracy,” in: Theory of Cubature Formulas and Applications of Functional Analysis to Some Problems of Mathematical Physics [in Russian], Novosibirsk (1973), pp. 31–35.

  4. V. I. Lebedev, “Quadrature formulas for a sphere with degree of accuracy 25–29,” Sib. Mat. Zh., 18, No. 1, 132–142 (1977).

    MATH  Google Scholar 

  5. V. I. Lebedev and D. N. Laikov, “Cubature formulas for a sphere of Gauss type of orders 65, 71, 77, 83, 89, 95, and 101,” in: Cubature Formulas and Their Applications [in Russian], Krasnoyarsk (1999), pp. 106–118.

  6. S. I. Konyaev, “Quadrature formulas on a sphere invariant with respect to icosahedral group,” in: Problems in Computational and Applied Mathematics [in Russian], Issue 32 (1975), pp. 69–76.

  7. S. I. Konyaev, “Quadratures of Gauss type for a sphere that are invariant with respect to the icosahedral group with inversion,” Mat. Zametki, 25, No. 4, 629–634 (1979).

    MATH  MathSciNet  Google Scholar 

  8. I. P. Mysovskikh, Interpolation Cubature Formulas [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  9. A. K. Ponomarenko, “Three cubature formulas with degree of accuracy 9 for a hyperoctahedron,” in: Cubature Formulas and Their Applications [in Russian], Krasnoyarsk (1999), pp. 150–158.

  10. A. K. Ponomarenko, “Two cubature formulas,” in: Cubature Formulas and Their Applications [in Russian], Krasnoyarsk (2003), pp. 133–138.

  11. S. B. Stoyanova, “Invariant cubature formulas of the seventh degree of accuracy for the hypersphere, ” in: Cubature Formulas and Their Applications [in Russian], Krasnoyarsk (1999), pp. 285–290.

  12. M. V. Noskov, “Cubature formulas for the approximate integration of periodic functions,” in: Cubature Formulas and Functional Equations [in Russian], Leningrad University, Leningrad (1985), pp. 15–24.

    Google Scholar 

  13. H. B. Dwight, Tables of Integrals and Other Mathematical Data, Macmillan, New York (1961).

    Google Scholar 

  14. V. F. Ignatenko, “On plane algebraic curves with symmetry axes,” Ukr. Geom. Sb., Issue 21, 31–33 (1978).

    Google Scholar 

  15. É. A. Shamsiev, “On invariant cubature formulas containing derivatives,” in: Numerical Integration and Related Problems [in Russian], Fan, Tashkent (1990), pp. 77–85.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tashkent University, Tashkent, Uzbekistan

    É. A. Shamsiev

Authors
  1. É. A. Shamsiev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 6, pp. 859–864, June, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shamsiev, É.A. On calculation of integrals over spherical domains. Ukr Math J 58, 974–980 (2006). https://doi.org/10.1007/s11253-006-0117-2

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-006-0117-2

Keywords

Search

Navigation