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...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/645345 |
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| author | Melusi Khumalo |
| author_facet | Melusi Khumalo |
| author_sort | Melusi Khumalo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6c24ad8ca9cc46b392f57edb8884349e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-6c24ad8ca9cc46b392f57edb8884349e2025-02-03T07:24:43ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/645345645345Dynamics of Numerics of Nonautonomous Equations with Periodic Solutions: Introducing the Numerical Floquet TheoryMelusi Khumalo0Department of Mathematics, University of Johannesburg, P.O. Box 17011, Doornfontein 2028, South AfricaNonautonomous 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.http://dx.doi.org/10.1155/2013/645345 |
| spellingShingle | Melusi Khumalo Dynamics of Numerics of Nonautonomous Equations with Periodic Solutions: Introducing the Numerical Floquet Theory Journal of Applied Mathematics |
| title | Dynamics of Numerics of Nonautonomous Equations with Periodic Solutions: Introducing the Numerical Floquet Theory |
| title_full | Dynamics of Numerics of Nonautonomous Equations with Periodic Solutions: Introducing the Numerical Floquet Theory |
| title_fullStr | Dynamics of Numerics of Nonautonomous Equations with Periodic Solutions: Introducing the Numerical Floquet Theory |
| title_full_unstemmed | Dynamics of Numerics of Nonautonomous Equations with Periodic Solutions: Introducing the Numerical Floquet Theory |
| title_short | Dynamics of Numerics of Nonautonomous Equations with Periodic Solutions: Introducing the Numerical Floquet Theory |
| title_sort | dynamics of numerics of nonautonomous equations with periodic solutions introducing the numerical floquet theory |
| url | http://dx.doi.org/10.1155/2013/645345 |
| work_keys_str_mv | AT melusikhumalo dynamicsofnumericsofnonautonomousequationswithperiodicsolutionsintroducingthenumericalfloquettheory |