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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
The Mathematical LaboratoryCambridge
P. Nicolson
Girton CollegeCambridge


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


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).

Research Article
Copyright © Cambridge Philosophical Society 1947

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