IMPROVED FINITE-DIFFERENCE SOLUTIONS OF THE DIFFUSION EQUATION FOR HEAT-CONDUCTION

A number of improved finite-difference solutions of explicit form have been reported recently. The choice of a particular solution of these improved explicit forms is dependent on the value of the non-dimensional time step as well as whether the process involves cooling or heating. The conditions for stable operation are clarified in the paper. Two new improved solutions of implicit forms are also reported in the paper. These new solutions give better accuracy compared to the conventional Crank-Nicolson and pure implicit methods, and have unrestricted stability.