Convergence and Validity of Time Expansion Solutions: A Comparison to Exact and Approximate Solutions1
- Jean-Yves Parlange2
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.Please view the pdf by using the Full Text (PDF) link under 'View' to the left.
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