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A method for the numerical integration of the linear diffusion equation

Published online by Cambridge University Press:  24 October 2008

D. R. Hartree
D. R. Hartree
Affiliation:
Cavendish LaboratoryCambridge
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Abstract

In one numerical method for integration of the diffusion equation in one dimension, the time derivative is replaced by a finite difference in a time interval, and the space derivative by the mean of its values at the beginning and end of the interval. This leads to a set of ordinary differential equations, one for each interval, which have to be solved in succession. Each of these equations is second-order with two-point boundary conditions; the process of integration from one end is severely unstable, the more so the smaller the tune interval. This paper is concerned with a practical, direct and stable method for solving them by integration of two first-order equations, one being integrated inwards and the other outwards, one boundary condition being satisfied in each integration. The extension to axially symmetrical diffusion is briefly considered.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 2 , April 1958 , pp. 207 - 213
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

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