Computing

, Volume 5, Issue 3, pp 221–245 | Cite as

Über die Konvergenzordnung von Differenzenverfahren, die parabolische Anfangsrandwertaufgaben approximieren

  • Burkhard Monien
Article
Received:

Zusammenfassung

Die Konvergenzordnung eines Differenzenverfahrens ist von den Differenzierbarkeitseigenschaften der Lösung der Differentialgleichung abhängig. Bei parabolischen Anfangsrandwertaufgaben werden diese durch die Anfangsfunktion bestimmt. Es wird das Verhalten der Konvergenzordnung in Abhängigkeit von der Anfangsfunktion untersucht.

On the rate of convergence of difference-schemes which approximate parabolic initial-value problems

Summary

The rate of convergence of a difference-scheme depends on the differentiability of the solution of the differential equation. In parabolic initial-value problems this is determined by the initial function. We examine the changing of the rate of convergence in dependence on the initial function.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. [1]
    Bari, H. K.: Über Basen im Hilbertraum. Doklady54, 383–386 (1946).Google Scholar
  2. [2]
    Juncosa-Young: On the Convergence of a Solution of a Difference Equation to a Solution of the Equation of Diffusion. Proc. Amer. Math. Soc.5, 168–178 (1954).Google Scholar
  3. [3]
    Juncosa-Young: Order of Convergence of Solutions of a Difference Equation. SIAM-Journal1, 111–135 (1953).Google Scholar
  4. [4]
    Juncosa-Young: On the Crank-Nicholson procedure for solving parabolic partial differential equations. Proc. Cambridge Phil. Soc.53, 448–461 (1957).Google Scholar
  5. [5]
    Michailov, B. P.: Über Rieszsche Basen imL 2 [0, 1]. Doklady114, 981–984 (1962).Google Scholar
  6. [6]
    Michlin, S. G.: The problem of the minimum of a quadratic functional. San Francisco, London, Amsterdam: Holden-Day. 1965.Google Scholar
  7. [7]
    Neumark, M. A.: Lineare Differentialoperatoren. Berlin: Akademie-Verlag. 1967.Google Scholar
  8. [8]
    Peetre-Thomeé: On the rate of convergence for discrete initial value problems. Math. Scand.21, 159–176 (1967).Google Scholar
  9. [9]
    Richtmyer-Morton: Difference Methods for Initial-Value Problems. New York-London-Sydney: Interscience Publishers. 1967.Google Scholar
  10. [10]
    Saul'yev, V. K.: Integration of Equations of Parabolic Type by the Method of Nets. Oxford, London: Pergamon Press. 1964.Google Scholar
  11. [11]
    Wasow, W.: On the accuracy of implicit difference approximations to the equation of heat flow. Math. Comp.12, 43–55 (1958).Google Scholar

Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • Burkhard Monien
    • 1
  1. 1.Rechenzentrum der Universität HamburgHamburg 13Bundesrepublik Deutschland

Personalised recommendations