DIFFERENCE SCHEMES FOR INITIAL-BOUNDARY VALUE PROBLEMS OF HYPERBOLIC SYSTEMS AND EXAMPLES OF APPLICATION

This papor is mainly concerned with numerical methods for inital-boundary value problems of quasi-linear hyperbolic systems in two independent variables. A few difference schemes applicable to any initial-boundary value problem have been given. Again, under quite weak conditions, it is proved that several type(?) of schemes with variable coefficients including those above-mentioned are stable with respect to initial values and boundary values. The unconditional stable second-order scheme of initial-boundary value probtlems presented here has been applied to calculate accurately some complicated physical process, such as interactions of discontinuities (shocks, contact discontinuities), automatically formed shocks. Finally, three numerical examples are provided. For some more computation results, and the generalization of the method to the case in three independent variables, [1] would be referred to.