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Feedback Stabilization Methods for the Numerical Solution of Systems of Ordinary Differential Equations
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 exploited and numerous illustrating
applications are presented for systems with a globally asymptotically stable
equilibrium point. The obtained results can be used for the control of the
global discretization error as well.Comment: 33 pages, 9 figures. Submitted for possible publication to BIT
Numerical Mathematic