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During the period covered by the Grants attention has been focused on three areas, all of them of importance in the successful application of implicit algorithms to Computational Fluid Dynamics (CFD): 1) The role of boundary conditions for implicit hyperbolic schemes; 2) The stability of hyperbolic Approximate Factorization schemes in three space dimensions; and 3) The rate of convergence to steady state of ADI methods. This report delineates the progress in each of the above enumerated areas. The details of the research will be found in reports and papers as referenced below for each of the tasks.