Completed Richardson extrapolation in space and time

The technique of Richardson extrapolation, which has previously been used on time-independent problems, is extended so that it can also be used on time-dependent problems. The technique presented is completed in the sense that the extrapolated solution is calculated at all spatial grid nodes which coincide with nodes of the finest grid considered. Numerical examples are presented when the technique is applied to the Lax–Wendroff and Crank–Nicholson finite difference schemes which are used to approximate solutions to the convection–diffusion equation. The examples show that extrapolation can be an easy and efficient way in which to produce accurate numerical solutions to time-dependent problems. © 1997 John Wiley & Sons, Ltd.