Skip to main content
SpringerLink
Log in

Investigation of economical difference systems for dynamical problems in elasticity theory in a class of nonsmooth solutions

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

Using an explicit central difference scheme, an economical difference system is constructed for the first boundary-value problem of the dynamical theory of elasticity for velocities and stresses. Estimates of the rate of convergence of the difference scheme is obtained under weak hypotheses on the smoothness of solutions to the differential problem.

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

Literature cited

  1. S. K. Godunov, Equations of Mathematical Physics [in Russian], Moscow (1971).

  2. I. N. Dzhuraer and M. N. Moskal'kov, “Investigation of the convergence of solutions to difference schemes with weights to a generalized solution of the equation for the vibrating string of class W2 2((Qτ)),” Diff. Uravn.,21, No. 12, 2145–2152 (1985).

    Google Scholar 

  3. A. Z. Ishmukhametov, “On the approximation of second-order hyperbolic differential-operator equations,” Zh. Vychisl. Mat. Mat. Fiz.,27, No. 8, 1154–1165 (1987).

    Google Scholar 

  4. M. N. Moskal'kov, V. L. Burkovskaya, and I. N. Dzhuraev, “Rate of convergence of discretization methods for the wave equation with generalized solutions,” Vychisl. Prikl. Mat., No. 57, 26–33 (1985).

    Google Scholar 

  5. M. N. Moskal'kov and D. Utebaev, “On the convergence of the ‘cross’ scheme for systems of acoustic equations,” Vychisl. Prikl. Mat., No. 56, 29–36 (1985).

    Google Scholar 

  6. M. N. Moskal'kov and D. Utebaev, “On the convergence of a central difference scheme for systems of twodimensional acoustic equations,” Vychisl. Prikl. Mat., No. 57, 48–57 (1985).

    Google Scholar 

  7. M. N. Moskal'kov and D. Utevaev, “On the convergence of a central difference scheme for dynamical problems in the theory of elasticity,” Diff. Uravn.,21, No. 7, 1238–1246 (1985).

    Google Scholar 

  8. A. A. Samarskii, Theory of Difference Schemes [in Russian], Moscow (1983).

  9. A. A. Samarskii, R. D. Lazarov, and V. L. Makarov, Difference Schemes for Differential Equations with Generalized Solutions [in Russian], Moscow (1987).

  10. G. Strang and G. Fix, Theory of the Finite-Element Method, Prentice-Hall, Englewood Cliffs (1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kiev State University, Kiev

    M. N. Moskal'kov & D. Utebaer

Authors
  1. M. N. Moskal'kov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Utebaer
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 16–23, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moskal'kov, M.N., Utebaer, D. Investigation of economical difference systems for dynamical problems in elasticity theory in a class of nonsmooth solutions. J Math Sci 67, 3042–3047 (1993). https://doi.org/10.1007/BF01098137

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01098137

Keywords

Search

Navigation