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2013 Dynamics of Numerics of Nonautonomous Equations with Periodic Solutions: Introducing the Numerical Floquet Theory
Melusi Khumalo
J. Appl. Math. 2013: 1-11 (2013). DOI: 10.1155/2013/645345

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.

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Melusi Khumalo. "Dynamics of Numerics of Nonautonomous Equations with Periodic Solutions: Introducing the Numerical Floquet Theory." J. Appl. Math. 2013 1 - 11, 2013. https://doi.org/10.1155/2013/645345

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.37046
MathSciNet: MR3056198
Digital Object Identifier: 10.1155/2013/645345

Rights: Copyright © 2013 Hindawi

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