THE SEMIGROUP STABILITY OF THE DIFFERENCE APPROXIMATIONS FOR INITIAL-BOUNDARY VALUE-PROBLEMS

For semidiscrete approximations and one-step fully discretized approximations of the initial-boundary value problem for linear hyperbolic equations with diagonalizable coefficient matrices, we prove that the Kreiss condition is a sufficient condition for the semigroup stability (or l(2) stability). Also, we show that the stability of a fully discretized approximation generated by a locally stable Runge-Kutta method is determined by the stability of the semidiscrete approximation.