An explicit conditionally stable finite difference equation for‐heat conduction problems

This paper reports a new explicit and conditionally stable finite difference equation for heat conduction. It predicts results with an accuracy comparable with or better than that obtainable by other methods. Stability of operation can be extended to any desired degree by subdividing the basic time step and increasing the number of nodes. Some existing difference equations are special cases of the new equation reported in this paper. The new solution has been tested by calculating the response of a slab to transient and progressive waves whose analytical solutions are known.