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

M. Khumalo | Zendy

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

Author(s) -

M. Khumalo

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/645345

Subject(s) - floquet theory , mathematics , simple (philosophy) , stability (learning theory) , collocation (remote sensing) , transformation (genetics) , dynamics (music) , mathematical analysis , nonlinear system , computer science , physics , biochemistry , philosophy , chemistry , epistemology , quantum mechanics , machine learning , gene , acoustics

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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