Computer Aided Analysis of Functional Differential Equations

8901893 Stech该项目涉及开发数值方法，旨在帮助理解由泛函微分方程(FDE)产生的动力学弱智型和中立型。将一种基于Liapunov-Schmidt的方法推广到中立型的FDE，并在数值和符号上实现。对几种应用于拟多项式的寻根技术的数值特征的研究将有助于深入了解必要的分叉数据的产生。用于跟踪单参数周期轨道族的通用代码将扩展到NFDE。将解决所用算法的收敛问题，以及矢量化和并行化问题。所开发的算法将在特殊类型的延迟差分方程组和电动力学模型上进行测试。

8901893 Stech The project concerns the development of numerical methods designed to aid in understanding the dynamics generated by functional differential equations (FDE) of both retarded and neutral type. A Liapunov-Schmidt based technique is to be extended to FDE of neutral type and implemented both numerically and symbolically. A study of the numerical characteristics of several rootfinding techniques applied to quasipolynomials will provide insight into the generation of the necessary bifurcation data. A general purpose code for the tracking of one-parameter families of periodic orbits will be extended to NFDE. Convergence questions for the algorithms used will be addressed, as will vectorization and parallelization issues. The developed algorithms will be tested on special classes of delay-difference equations and a model from electrodynamics.