A periodic boundary value problem with switchings under nonlinear perturbations
Abstract We investigate the existence of solutions of weakly nonlinear periodic boundary value problems for systems of ordinary differential equations with switchings and the construction of these solutions. We consider the critical case where the equation for the generating constants of a weakly no...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-04-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-023-01734-1 |
| _version_ | 1797836388762124288 |
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| author | Peter Benner Sergey Chuiko Alexander Zuyev |
| author_facet | Peter Benner Sergey Chuiko Alexander Zuyev |
| author_sort | Peter Benner |
| collection | DOAJ |
| description | Abstract We investigate the existence of solutions of weakly nonlinear periodic boundary value problems for systems of ordinary differential equations with switchings and the construction of these solutions. We consider the critical case where the equation for the generating constants of a weakly nonlinear periodic boundary-value problem with switchings does not turn into an identity. We improve the classification of critical and noncritical cases and construct an iterative algorithm for finding solutions of weakly nonlinear periodic boundary value problems with switchings in the critical case. As examples of application of the constructed iterative scheme, we obtain approximations to the solutions of a periodic boundary value problem for the mathematical model of nonisothermal chemical reactions. To check the accuracy of the proposed approximations, we evaluate discrepancies in the original equation. |
| first_indexed | 2024-04-09T15:08:02Z |
| format | Article |
| id | doaj.art-f8a0ac2240ad40548cbb03d74a62a1f1 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-09T15:08:02Z |
| publishDate | 2023-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-f8a0ac2240ad40548cbb03d74a62a1f12023-04-30T11:22:37ZengSpringerOpenBoundary Value Problems1687-27702023-04-012023111210.1186/s13661-023-01734-1A periodic boundary value problem with switchings under nonlinear perturbationsPeter Benner0Sergey Chuiko1Alexander Zuyev2Max Planck Institute for Dynamics of Complex Technical SystemsMax Planck Institute for Dynamics of Complex Technical SystemsMax Planck Institute for Dynamics of Complex Technical SystemsAbstract We investigate the existence of solutions of weakly nonlinear periodic boundary value problems for systems of ordinary differential equations with switchings and the construction of these solutions. We consider the critical case where the equation for the generating constants of a weakly nonlinear periodic boundary-value problem with switchings does not turn into an identity. We improve the classification of critical and noncritical cases and construct an iterative algorithm for finding solutions of weakly nonlinear periodic boundary value problems with switchings in the critical case. As examples of application of the constructed iterative scheme, we obtain approximations to the solutions of a periodic boundary value problem for the mathematical model of nonisothermal chemical reactions. To check the accuracy of the proposed approximations, we evaluate discrepancies in the original equation.https://doi.org/10.1186/s13661-023-01734-1Periodic boundary value problemEquation for the generating constantsCritical caseNonlinear chemical reaction model |
| spellingShingle | Peter Benner Sergey Chuiko Alexander Zuyev A periodic boundary value problem with switchings under nonlinear perturbations Boundary Value Problems Periodic boundary value problem Equation for the generating constants Critical case Nonlinear chemical reaction model |
| title | A periodic boundary value problem with switchings under nonlinear perturbations |
| title_full | A periodic boundary value problem with switchings under nonlinear perturbations |
| title_fullStr | A periodic boundary value problem with switchings under nonlinear perturbations |
| title_full_unstemmed | A periodic boundary value problem with switchings under nonlinear perturbations |
| title_short | A periodic boundary value problem with switchings under nonlinear perturbations |
| title_sort | periodic boundary value problem with switchings under nonlinear perturbations |
| topic | Periodic boundary value problem Equation for the generating constants Critical case Nonlinear chemical reaction model |
| url | https://doi.org/10.1186/s13661-023-01734-1 |
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