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It is of interest to determine whether loosely coupled multiprocessors can be profitably used for the solution of larger numerical problems. We present here a performance evaluation of the gain obtained by solving partial differential equation systems on such an architecture. The experimental setting is an LSI 11 based multimicroprocessor system using a fiber optics local area network designed and implemented at Laboratoire de Recherche en Informatique, Université Paris-Sud. The paper includes a discussion of the numerical methods and of their implementation, a performance model of the parallel processing system, and measurements taken on the experimental system. The experimentally validated theoretical results confirm the interest of our approach based on performance models.