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

Source abstract

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).