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On the Crank-Nicolson procedure for solving parabolic partial differential equations

Published online by Cambridge University Press:  24 October 2008

M. L. Juncosa  and
David Young
M. L. Juncosa
Affiliation:
RAND Corporation Santa Monica, California
David Young
Affiliation:
University of Maryland CollegePark, Maryland
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Abstract

Proof of convergence of the Crank-Nicolson procedure, an ‘implicit’ numerical method for solving parabolic partial differential equations, is given for the case of the classical ‘problem of limits’ for one-dimensional diffusion with zero boundary conditions. Orders of convergence are also given for different classes of initial functions. Results do not support the validity of so-called h2-extrapolation in some cases.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 2 , April 1957 , pp. 448 - 461
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

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