Stability and accuracy of numerical solutions of the heat flow equation

Abstract

The merits of different finite difference representations of the heat flow equation and a convection boundary condition equation are discussed in terms of the stability and accuracy of the solutions they yield. A new method of deriving a condition for stability is given. This is applied to examples of heat conduction involving variable thermal diffusivity and heat transfer by convection at the surface. Some finite difference forms of this boundary condition impose stability criteria which are stricter than, or additional to, that required in the case of a prescribed surface temperature. A new finite difference representation of the surface heat flux equation is discussed.