Symbolic Computation and Differential Equations

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The project is concerned with three related objectives: Objective 1. Develop data structures and efficient algorithms for the exact symbolic computation of approximate solutions of differential equations. Objective 2. Apply these algorithms to develop mixed symbolic- numeric integration schemes to integrate trajectories of nonlinear systems. Objective 3. Apply these algorithms and schemes to problems in bifurcation theory, normal forms, and nonlinear realization theory. In the long term, new algorithms in this area will impact technology by leading to the design of better robots, aircraft and satellites.