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This article in SSSAJ

  1. Vol. 39 No. 1, p. 3-6
     
    Received: Sept 3, 1974
    Published: Jan, 1975


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doi:10.2136/sssaj1975.03615995003900010006x

Convergence and Validity of Time Expansion Solutions: A Comparison to Exact and Approximate Solutions1

  1. Jean-Yves Parlange2

Abstract

Abstract

The convergence of series solutions for the diffusion equation by time expansion is discussed quantitatively, on the basis of the linear and delta function solutions for a spherical cavity. It is shown that convergence alone is a poor criterion to justify the validity of the series solutions. A counter example, diffusion in the presence of an impervious wall, shows that the series may converge for all times but be entirely erroneous. By comparison an approximate integral technique yields a solution which agrees very well with the exact result.

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