MAXIMUM-NORM ESTIMATES OF RATE OF CONVERGENCE OF DISSIPATIVE DIFFERENCE SCHEMES FOR STRICTLY HYPERBOLIC SYSTEMS

The rate of convergence in maximum-norm of dissipative difference schemes for strictly hyperbolic systems is given in terms of L//1-smoothness of the initial data. Estimates over the set of mesh-points, and the effect of smoothing the initial data are also considered. For functions with only a finite number of isolated singularities, the estimates obtained often give considerable improvements over those given in terms of L// infinity -smoothness of the initial data.