Mathematical Sciences Computing Research Environment

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The Department of Systems Science and Mathematics at Washington University, St. Louis, will purchase Sun Microsystems Graphics Workstation equipment which will be dedicated to the support of research in the mathematical sciences. The equipment will be used for several research projects, including in particular: 1. Computational theory of Riccati partial differential equations, fundamental to the control of nonlinear systems, directed especially to a visualization of their classical blow- ups and nonlinear shock waves; 2. Optimization for probabilistic systems, in which the objective function is estimated by Monte Carlo simulation, which is computation intensive; 3. The p-version of the finite element method, pioneered here and now being extended to nonlinear and time-varying problems; 4. Symbolic algebraic computation for nonlinear control theory, using Lie algebra and formal power series methods, and numerical experimentation with resulting new invariant-preserving integration methods, with graphic output.