Skip to main content
SpringerLink
Log in

A stable explicit difference approximation of the one-dimensional diffusion equation

Ein stabiles explizites Diffrenzeverfahren zur Lösung der eindimensionalen Wärmeleitungsgleichung

  • Published:
Computing Aims and scope Submit manuscript

Abstract

An explicit difference approximation of the one-dimensional diffusion equation equation, which is stable for any choice of the difference gird and has a comparatively small truncation error, is described. A smoothing formula, which makes the practical use of this method possible, is given.

Zusammenfassung

Zuerst wird ein explizites Differenzenverfahren beschrieben, das die eindimensionale Wärmeleitungs-gleichung approximiert und bei willkürlicher Wahl des Differenzengitters stabil ist. Dann folgt die Beschreibung eines Glättungsverfahrens, das die praktische Anwendung dieser Methode ermöglicht.

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. Bulirsch, R., und J. Stoer: Fehlerabschätzungen und Extrapolation mit rationalen Funktionen bei Verfahren vom Richardson-Typus. Numerische Mathematik6, 413–427 (1964).

    Google Scholar 

  2. Du Fort, E. C., and S. P. Frankel: Stability conditions in the numerical treatment of parabolic differential equations. Mathematical Tables and Other Aids to Computation7, 135–152 (1953).

    Google Scholar 

  3. Forsythe, G. E., and W. R. Wasow: Finite-Difference Methods for Partial Differential Equations. New York: J. Wiley. 1960.

    Google Scholar 

  4. Gordon, P.: Nonsymetric difference equations. Journal of the Society for Industrial and Applied Mathematics2, 667–673 (1965).

    Google Scholar 

  5. Jourbert, G. R.: Explicit difference approximations of the one-dimensional diffusion equation, using a smoothing technique. Numerische Mathematik17, 409–430 (1971).

    Google Scholar 

  6. Joubert, G. R.: Explicit difference approximations of Du Fort-Frankel type of the one-dimensional diffusion equation. Numerische Mathematik18, 8–25 (1971).

    Google Scholar 

  7. Richtmyer, R. D., and K. W. Morton: Difference Methods for Initial-Value Problems. 2nd edition. New York: Interscience Publishers. 1967.

    Google Scholar 

  8. Saul'yev, V. K.: Integration of Equations of Parabolic Type by the Method of Nets. Oxford: Pergamon Press. 1964.

    Google Scholar 

  9. Stetter, H. J.: Asymptotic expansions for the error of discretization algorithms for the linear functional equations. Numerische Mathematik7, 18–31 (1965).

    Google Scholar 

  10. Werner, W.: Numerical solution of systems of quasilinear hyperbolic differential equations by means of the method of nebencharacteristics in combination with extrapolation methods. Numerische Mathematik11, 151–169 (1968).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of South Africa, P. O. Box 392, Pretoria, South Africa

    G. R. Joubert

Authors
  1. G. R. Joubert
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

With 1 Figure

Rights and permissions

Reprints and permissions

About this article

Cite this article

Joubert, G.R. A stable explicit difference approximation of the one-dimensional diffusion equation. Computing 11, 315–325 (1973). https://doi.org/10.1007/BF02239158

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02239158

Keywords

Search

Navigation