Title

On the Long Time Behavior of Approximating Dynamical Systems

Abstract

In this paper we consider the impact of using "time marching" numerical schemes for computing asymptotic solutions of nonlinear differential equations. We show that stable and consistent approximating schemes can produce numerical solutions that do not correspond to the correct asymptotic solutions of the differential equation. In addition, we show that this problem cannot be avoided by placing additional side conditions on the boundary value problem, even if the numerical scheme preserves the side conditions at every step. Examples are given to illustrate the problems that can arise and the implications of using such methods in control design are discussed.

Department(s)

Mathematics and Statistics

Document Type

Book - Chapter

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2003 Birkhauser, All rights reserved.

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