On the Long Time Behavior of Approximating Dynamical Systems
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.
J. A. Burns and J. R. Singler, "On the Long Time Behavior of Approximating Dynamical Systems," Control and Estimation of Distributed Parameter Systems, Birkhauser, Jan 2003.
Mathematics and Statistics
Book - Chapter
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