STABILITY-CRITERIA FOR A GENERAL-CLASS OF FINITE-DIFFERENCE SCHEMES

The von Neumann stability analysis is performed on a generalized class of two-level space-centered finite difference schemes known as Lerat- Peyret schemes. In the present study, these schemes are used to solve the convection-diffusion equation in an effort to obtain a better asse ssment of the accuracy of such schemes. Exact stability criteria are d erived for each of five different schemes applied to the Burgers equat ion. Exact results for the amplification factor and phase error are pl otted for several values of Courant number and diffusion parameter for each scheme. These exact results, which are presented here for the fi rst time, are extremely valuable in assessing the dissipation and disp ersion characteristics of each scheme. This study shows promise for ex tending this analysis to the Navier-Stokes equations.