Fritz John pp 389-402 | Cite as

Numerical solution of the equation of heat conduction for preceding times

  • Fritz John
Part of the Contemporary Mathematicians book series (CM)


The problem of determining numerically a positive solution u(x, t) of the equation ut = uxx for - T ≦ t ≦ 0 from approximate values of u(x, 0) = f(x) is discussed. For a particular computational scheme estimates for the error are derived, which depend on t, T, the maximum error s in the approximation for f, and on the maximum of f. It turns out that although the problem is incorrectly set in the sense of HADAMARD a satisfactory numerical solution can be obtained due to the a priori assumption u ≧ 0.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. V. WIDDER, The convolution transform, «Bull. Am. Math. Soc. », v. 60 (1954),pp. 444–456.CrossRefGoogle Scholar
  2. [2]
    R. COURANT and D. HILBERT, Methoden der mathematischen Physik, (Springer, 1937).CrossRefGoogle Scholar
  3. [3]
    C. PUCCI, Studio col metodo delle differenze di un problema di Caachy relativo ad equazioni a derivate parziali del secondo ordine di tipo parabolico , « Annali della Scuola Normale Superiore di Pisa», Serie III, vol. 7 (1953), 205–215. Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Fritz John
    • 1
  1. 1.New YorkUSA

Personalised recommendations