Continuum shock profiles for discrete conservation laws II: Stability

We show that the continuum shock profiles for dissipative difference scheme s constructed in Part I are nonlinearly stable. It is shown first that the profiles have the conservation property, obtained as the limit of the discr ete version for profiles with nearby rational, quasi-Diophantine speeds. Th is allows us to formulate antidifferencing of the schemes and to apply a ge neralization of the pointwise approach for viscous conservation laws for th e stability analysis. (C) 1999 John Wiley & Sons, Inc.