Symbolic Computation and Differential Equations

该项目涉及三个相关目标： 目的1. 开发数据结构和高效算法 的近似解的精确符号计算 微分方程 目标2. 应用这些算法开发混合符号- 数值积分方案， 非线性系统 目标3. 将这些算法和方案应用于 分歧理论，规范形，非线性实现 理论 从长远来看，这一领域的新算法将影响 通过设计更好的机器人、飞机 和卫星。

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.