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

Melusi Khumalo

Journal of Applied Mathematics, 2013, vol. 2013, 1-11

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:645345

DOI: 10.1155/2013/645345

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