Computer Aided Analysis of Functional Differential Equations

点击翻译按钮获取中文摘要

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.