Skip to main content
Log in

Uniform stability of a class of parabolic difference operators

  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

Conditions on a class of parabolic difference operators are given which are sufficient for maximumnorm stability, uniform in the mesh-widths. This paper is a generalization of a previous result by Hakberg [4].

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

Access this article

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. A. Beurling,Sur les integrales de Fourier absolument convergentes et leur application à une transformation functionelle, IX Congrès des Math. Scandinaves, Helsingfors (1938), 345–366.

  2. A. Beurling and H. Helson,Fourier-Stieltjes transforms with bounded powers, Math. Scand. 1. (1953), 120–126.

    Google Scholar 

  3. P. Brenner and V. Thomée,Estimates near discontinuities for some difference schemes, Math. Scand. 28 (1971), 329–340.

    Google Scholar 

  4. B. Hakberg,Uniformly maximumnorm stable difference schemes, BIT 10 (1970), 266–276.

    Google Scholar 

  5. L. Hörmander,Estimates for translation invariant operators on L p -spaces, Acta Math. 104 (1960), 93–140.

    Google Scholar 

  6. B. Kjellberg, Ein Momentenproblem, Ark. Mat. Astr. Fys. 29A, 2 (1943), 1–33.

    Google Scholar 

  7. W. Rudin,Fourier analysis on groups (Interscience Tracts in Pure and Applied Mathematics 12), Interscience Publishers, New York, London, 1962.

    Google Scholar 

  8. S. I. Serdjukova,The uniform stability of a sixpoint scheme of increased order of accuracy for the heat conduction equation, Ž. Vyčisl. Mat. i Mat. Fiz., 7 (1967).

  9. L. Wahlbin,L p -estimates for Friedrichs' scheme for strongly hyperbolic systems in two space variables, to appear.

  10. R. S. Varga,On higher order stable implicit methods for solving parabolic partial differential equations, J. Math. and Phys., 40 (1961), 220–231.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nordmark, S. Uniform stability of a class of parabolic difference operators. BIT 14, 314–325 (1974). https://doi.org/10.1007/BF01933231

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01933231

Keywords

Navigation