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.


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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