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There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation like one obtained from the ADM equations. We shall discuss the wellposedness of the Cauchy problem for such systems and their advantage in numerical calculations.

Some Mathematical and Numerical Questions Connected with First and Second Order Time-Dependent Systems of Partial Differential Equations