Numerical Analysis of Dynamical Systems
نویسنده
چکیده
This survey concentrates on exposition of fundamental mathematical principles and their application to the numerical analysis of examples. There is a strong interplay between dynamical systems theory and computational analysis of dynamical systems. The theory provides a framework for interpreting numerical observations and foundations for algorithms. Apparent discrepancies between computational output and theoretical expectations point to areas where phenomena have been overlooked in the theory, areas where algorithms produce misleading results, and areas where the relationship between theory and computation is more subtle than anticipated. Several examples of simple systems are used in this article to illustrate seeming differences between computation and theory. ∗Mathematics Department, Cornell University, Ithaca, NY 14853. This work was partially supported by grants from the Department of Energy, Air Force Office of Scientific Research and the National Science Foundation
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