Dynamics of Numerics of Nonautonomous Equations with Periodic Solutions : Introducing the Numerical Floquet Theory

Abstract EN

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.