Approximation and Computation of Lyapunov Exponents, Global Errors, and Functional Traveling Waves

货车Vleck 9973393研究员和他的同事研究计算微分方程中的问题：跟踪和初值问题的全局误差分析的相关主题，稳定性信息和李雅普诺夫指数的计算，以及格微分方程的分析和计算，即，空间离散时间连续的微分方程。 该项目的中心主题是将动力系统思想与数值分析思想相结合。 重点是有效的，准确的数值技术的发展和分析，并在分析和计算技术，帮助确定有趣的微分方程的动力学性质。研究员和他的同事研究方法，了解在微分方程的数值计算过程中发生的错误的传播。 这种理解是基本的，因为物理和生物系统的模型通常使用计算技术来解决。 格点微分方程的研究在材料建模领域有着广泛的应用。 正在考虑的模型允许包括微观和宏观效应，这将变得更加重要，因为计算机技术的进步允许更大，更复杂的材料模型。

Van Vleck9973393The investigator and his colleagues study issues in computational differential equations: shadowing and related topics of global error analysis for initial value problems, computation of stability information and Lyapunov exponents, and analysis and computation of lattice differential equations, i.e., differential equations that are discrete in space and continuous in time. This project has as a central theme the combination of dynamical systems ideas with numerical analysis ideas. The focus is on the development and analysis of efficient, accurate numerical techniques and on analytical and computational techniques that help identify interesting dynamic properties of differential equations.The investigator and his colleagues study methods for understanding the propagation of errors that occur during the numerical computation of differential equations. This understanding is fundamental because models of physical and biological systems are often solved using computational techniques. The research on lattice differential equations has applications in the area of materials modeling. The models being considered allow for the inclusion of both microscopic and macroscopic effects, which will become more important as advances in computer technology allow for larger, more sophisticated models of materials.