Asymptotic behaviour of coupled systems in discrete and continuous time
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtai...
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| Format: | Journal article |
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Springer
2016
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| _version_ | 1797105316232429568 |
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| author | Paunonen, L Seifert, D |
| author_facet | Paunonen, L Seifert, D |
| author_sort | Paunonen, L |
| collection | OXFORD |
| description | This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time. |
| first_indexed | 2024-03-07T06:45:45Z |
| format | Journal article |
| id | oxford-uuid:facb657c-df7d-46d3-9677-625fe5b61da5 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:45:45Z |
| publishDate | 2016 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:facb657c-df7d-46d3-9677-625fe5b61da52022-03-27T13:08:54ZAsymptotic behaviour of coupled systems in discrete and continuous timeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:facb657c-df7d-46d3-9677-625fe5b61da5Symplectic Elements at OxfordSpringer2016Paunonen, LSeifert, DThis paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time. |
| spellingShingle | Paunonen, L Seifert, D Asymptotic behaviour of coupled systems in discrete and continuous time |
| title | Asymptotic behaviour of coupled systems in discrete and continuous time |
| title_full | Asymptotic behaviour of coupled systems in discrete and continuous time |
| title_fullStr | Asymptotic behaviour of coupled systems in discrete and continuous time |
| title_full_unstemmed | Asymptotic behaviour of coupled systems in discrete and continuous time |
| title_short | Asymptotic behaviour of coupled systems in discrete and continuous time |
| title_sort | asymptotic behaviour of coupled systems in discrete and continuous time |
| work_keys_str_mv | AT paunonenl asymptoticbehaviourofcoupledsystemsindiscreteandcontinuoustime AT seifertd asymptoticbehaviourofcoupledsystemsindiscreteandcontinuoustime |