A comparison of two explicit time integration schemes applied to the transient heat equation

The forward-central (forward in time, central differencing in space) scheme and the Dufort-Frankel scheme applied to the transient heat equation are discussed. The Dufort-Frankel scheme is shown to be unable to damp the oscillation of the high oscillatory 2-delta-x wave. It can even become unstable for this wave which may be produced by the initial conditions, nonlinear interactions, or other forcing. On the other hand, the forward-central scheme works well if mu is less than 0.5. Examples of the applications of these schemes in fluid dynamics are also presented. It is also noted that none of the schemes are accurate for the high-frequency short wave.