Restoring Orders of Accuracy for Multilevel Schemes for Non-linear Hyperbolic Systems in Many Space Variables

In this paper boundary procedures are discussed for a new secondorder accurate method, developed in Morris (1972) and Zwas,Eilon & Gottlieb (1972), for non-linear hyperbolic systemsin two space variables. This method is a multilevel scheme ofthe same type as those of Strang, (1964, 1968). It is shownthat the straightforward method of incorporating boundary datagives, in general, only locally first order accurate values.A boundary procedure which preserves local second order accuracyis developed. The method is also extended to systems in manyspace variables. The results of some numerical experiments arereported.