Application of Richardson extrapolation for multi-dimensional advection equations

A Crank-Nicolson type scheme, which is of order two with respect to all independent variables, is used in the numerical solution of multi-dimensional advection equations. Normally, the order of accuracy of any numerical scheme can be increased by one when the well-known Richardson Extrapolation is used. It is proved that in this particular case the order of accuracy of the combined numerical method, the method consisting of the Crank-Nicolson scheme and the Richardson Extrapolation, is not three but four.