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A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type

Published online by Cambridge University Press:  24 October 2008

J. Crank  and
P. Nicolson
J. Crank
Affiliation:
The Mathematical LaboratoryCambridge
P. Nicolson
Affiliation:
Girton CollegeCambridge
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Extract

This paper is concerned with methods of evaluating numerical solutions of the non-linear partial differential equation

where

subject to the boundary conditions

A, k, q are known constants.

Equation (1) is of the type which arises in problems of heat flow when there is an internal generation of heat within the medium; if the heat is due to a chemical reaction proceeding at each point at a rate depending upon the local temperature, the rate of heat generation is often defined by an equation such as (2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 43 , Issue 1 , January 1947 , pp. 50 - 67
Copyright
Copyright © Cambridge Philosophical Society 1947

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References

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