Application of Richardson extrapolation for multi-dimensional advection equations
A CrankNicolson 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 CrankNicolson scheme and the Richardson Extrapolation, is not three but four.
richardson extrapolation multi-dimensional advection order of accuracy cranknicolson numerical scheme