Computer Aided Analysis of Functional Differential Equations

函数微分方程的计算机辅助分析

• 批准号: 8901893
• 负责人: Harlan Stech
• 金额: $ 4.75万
• 依托单位: University of Minnesota Duluth
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901893&HistoricalAwards=false
• 关键词: Computer; Aided; Analysis; Functional; Differential

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.

8901893 Stech 该项目涉及数值方法的开发，旨在帮助理解延迟型和中性型函数微分方程 (FDE) 生成的动力学。 基于 Liapunov-Schmidt 的技术将扩展到中性类型的 FDE，并以数字和符号方式实现。 对应用于拟多项式的几种求根技术的数值特性的研究将有助于深入了解必要的分岔数据的生成。 用于跟踪周期轨道单参数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。 开发的算法将在特殊类别的延迟差分方程和电动力学模型上进行测试。