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Dynamics of numerics of nonautonomous equations with periodic solutions: introducing the numerical Floquet theory. (English) Zbl 1266.37046

Summary: Nonautonomous systems with periodic solutions are encountered frequently in applications. In this paper, we will consider simple systems whose solutions are periodic with a known period. Their transformation under linearized collocation methods is investigated, using a technique called stroboscopic sampling, a discrete version of the well-known Poincaré map. It is shown that there is an inextricable relationship between AN stability (or BN stability) of the numerical methods and the correct qualitative behaviour of solutions.

MSC:

37M99 Approximation methods and numerical treatment of dynamical systems
37C60 Nonautonomous smooth dynamical systems
37C27 Periodic orbits of vector fields and flows
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