We propose to use a supercomputer facility in order to carry out the following research projects: 1. Preconditioners and decomposition of large systems of equations. 2. Improvements of the ADI algorithm in relation to 3- dimensional turbulant flows. 3. Optimal pursuit problem for satellites in general orbits. 4. Lie symmetries of differential equations. Requested CPU time: 25 hours. Duration: 24 months. Centers requested: Cornell or Princeton.