Stability and A-stability of dissipative difference scheme for strongly hyperbolic systems

In this paper we give a stability theorem and an A-stability theorem of dis sipative difference schemes for strongly hyperbolic systems with variable c oefficients. The A-stability theorem is considered only in the case that th ose coefficients are differ from constant coefficients by sufficiently smal l variable parts. We prove them under the assumption that symbols of scheme s have smooth symmetrizers, by using the theory of pseudo-difference operat ors.