Von Neumann stability conditions for the convection-diffusion equation

A method is presented to easily derive von Neumann stability conditions for a wide variety of time discretization schemes for the convection-diffusion equation. Spatial discretization is by the (c-scheme or the fourth-order central scheme. The use of the method is illustrated by application to multistep, Runge-Kutta and implicit-explicit methods, such as are in current use for flow computations, and for which, with few exceptions, no sufficient von Neumann stability results are available. 1