Dynamics of numerics of nonautonomous equations with periodic solutions: Introducing the numerical floquet theory

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. © 2013 melusi khumalo.