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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 645345, 11 pages
http://dx.doi.org/10.1155/2013/645345
Research Article

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

Department of Mathematics, University of Johannesburg, P.O. Box 17011, Doornfontein 2028, South Africa

Received 22 September 2012; Revised 2 March 2013; Accepted 26 March 2013

Academic Editor: Alberto Cabada

Copyright © 2013 Melusi Khumalo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.