Abstract
The Courant-Friedrichs-Lewy condition (CFL condition) is one of the most important concepts in the analysis of the finite difference method applied to linear hyperbolic partial differential equations. It is sometimes misunderstood as a sufficient condition for stability of difference schemes, although it is a necessary condition for convergence. We note, in this study, the proper meaning of the CFL condition and show numerical instability of a finite difference scheme even under the CFL condition. We also show the variety of numerical instability within computing environments based on IEEE754.
