A critical analysis of the modified equation technique of Warming and Hyett

The modified equation technique of Warming and Hyett (1974), which evaluates the behavior of a difference scheme by means of the coefficients of a certain modified equation, established a link between such coefficients and the multiplication factor obtained from the von Neumann analysis. It follows from this pioneering work that modified equations should be derived from the difference scheme, rather than from the original differential equation; a rigorous investigation is presently made of this link without resort to their original interpretation. Only partial validity is establishable for the case of multilevel schemes.