Computer Aided Analysis of Functional Differential Equations

该项目涉及数值方法的发展，旨在帮助理解弱智型和中性型的泛函微分方程（FDE）产生的动力学。​将一种基于Liapunov-Schmidt的技术扩展到中性类型的FDE，并以数值和符号两种方式实现。对应用于拟多项式的几种寻根技术的数值特征的研究将提供对生成必要的分岔数据的洞察。一个用于周期轨道单参数族跟踪的通用代码将扩展到NFDE。所使用的算法的收敛问题，以及向量化和并行化问题将被解决。开发的算法将在特殊类型的延迟差分方程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.