ON DESTABILIZING IMPLICIT FACTORS IN DISCRETE ADVECTION-DIFFUSION EQUATIONS

In the present paper, we find necessary and sufficient stability condi tions for a simple one-time step finite difference discretization of a n N-dimensional advection-diffusion equation. Furthermore, it is shown that when the implicit factors differ in each direction, a strange be havior occurs: By increasing one implicit factor in only one direction , a stable scheme can become unstable. It is thus suggested to use a s ingle implicit direction (for efficient computing), or the same implic it factor in each direction. (C) 1994 Academic Press, Inc.