Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

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

J. Cranka1 and P. Nicolsona2

a1 The Mathematical Laboratory Cambridge

a2 Girton College Cambridge

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

S0305004100023197_eqn001

where

S0305004100023197_eqn002

subject to the boundary conditions

S0305004100023197_eqn003

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).

(Received March 20 1946)