Feedback stabilization methods for the numerical solution of systems of ordinary differential equations

L. Grüne, I. Karafyllis: Feedback stabilization methods for the numerical solution of systems of ordinary differential equations
in: Proceedings of the International Conference on Numerical Analysis ans Applied Mathematics ICNAAM 2009, AIP Conference Proceedings 1168, Rethymno, Crete, Greece, 2009, 152 - 155

Smart-Link: http://scitation.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=1168&Issue=1
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Abstract:

In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools from nonlinear control theory. Lyapunov-based and Small-Gain feedback stabilization methods are presented for systems with a globally asymptotically stable equilibrium point. Proceeding this way, we derive conditions under which the step size selection problem is solvable (including a nonlinear generalization of the well-known A-stability property for the implicit Euler scheme) as well as step size selection strategies for several applications.

See also the extended journal version of the paper.

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