Skip to main content
SpringerLink
Log in

Stability and convergence of a system of nonlinear difference equations

  • I. Numerical Methods
  • Published:
Computational Mathematics and Modeling Aims and scope Submit manuscript

Abstract

We investigate stability and convergence of solutions of a system of nonlinear difference equations approximating a system of nonlinear parabolic equations. A linear system of similar structure is also considered. An energy norm is constructed for the linear system, and stability and convergence in this norm are proved under certain necessary conditions. Stability and convergence of solutions of the nonlinear system of difference equations are proved in a similar norm.

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. A. D. Lyashko and E. M. Fedotov, "On correctness of nonlinear two-layer operator-difference schemes,"Diff. Uravn. 17, No. 7, 1304–1316 (1981).

    Google Scholar 

  2. V. N. Abrashin, "On one class of difference schemes for nonlinear nonstationary problems of mathematical physics," Preprint No. 17(142), Inst. Mat. Akad. Nauk BSSR, Minsk (1982).

    Google Scholar 

  3. V. N. Abrashin and V. V. Drits, "Stable difference schemes in gas dynamics," Preprint No. 8(109), Inst. Mat. Akad. Nauk BSSR, Minsk (1981).

    Google Scholar 

  4. A. V. Gordeev, L. I. Rudakov, and V. Yu. Shuvaev, "Displacement of the magnetic field by a cloud of hot electrons,"Zh. Éksp. Teor. Fiz. 85, No. 1(7), 155–165 (1983).

    Google Scholar 

  5. N. V. Ardelyan and S. V. Chernigovskii, "On stability of one operator-difference scheme defined on a direct sum of spaces,"Vestn. Mosk. Gos. Univ., No. 1, 32–37 (1984).

    Google Scholar 

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

    Google Scholar 

  7. A. A. Samarskii and A. V. Gulin,Stability of Difference Schemes [in Russian], Nauka, Moscow (1973).

    Google Scholar 

Download references

Authors
  1. V. S. Aref'ev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Metody Matematicheskogo Modelirovaniya, Avtomatizatsiya Obrabotki Nablyudenii i Ikh Primeneniya, pp. 120–127, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aref'ev, V.S. Stability and convergence of a system of nonlinear difference equations. Comput Math Model 1, 143–148 (1990). https://doi.org/10.1007/BF01129056

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01129056

Keywords

Search

Navigation