Perturbation Methods for Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2003
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In nonlinear problems, essentially new phenomena occur which have no place in the corresponding linear problems. Therefore, in the study of nonlinear problems the major purpose is not so much to introduce methods that improve the accuracy of linear methods, but to focus attention on those features of the nonlinearities that result in distinctively new phenomena. Among the latter are - * existence of solutions ofperiodic problems for all frequencies rather than only a setofcharacteristic values, * dependenceofamplitude on frequency, * removal ofresonance infinities, * appearance ofjump phenomena, * onsetofchaotic motions. On the other hand, mathematical problems associated with nonlinearities are so complex that a comprehensive theory of nonlinear phenomena is out of the question.' Consequently, one practical approach is to settle for something less than complete generality. Thus, one gives up the study of global behavior of solutions of a nonlinear problem and seeks nonlinear solutions in the neighborhood of (or as perturbations about) a known linear solution. This is the basic idea behind a perturbative solutionofa nonlinear problem |
| Beschreibung: | 1 Online-Ressource (XIV, 354 p) |
| ISBN: | 9781461200475 9781461265887 |
| DOI: | 10.1007/978-1-4612-0047-5 |
Internformat
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| 500 | |a In nonlinear problems, essentially new phenomena occur which have no place in the corresponding linear problems. Therefore, in the study of nonlinear problems the major purpose is not so much to introduce methods that improve the accuracy of linear methods, but to focus attention on those features of the nonlinearities that result in distinctively new phenomena. Among the latter are - * existence of solutions ofperiodic problems for all frequencies rather than only a setofcharacteristic values, * dependenceofamplitude on frequency, * removal ofresonance infinities, * appearance ofjump phenomena, * onsetofchaotic motions. On the other hand, mathematical problems associated with nonlinearities are so complex that a comprehensive theory of nonlinear phenomena is out of the question.' Consequently, one practical approach is to settle for something less than complete generality. Thus, one gives up the study of global behavior of solutions of a nonlinear problem and seeks nonlinear solutions in the neighborhood of (or as perturbations about) a known linear solution. This is the basic idea behind a perturbative solutionofa nonlinear problem | ||
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Datensatz im Suchindex
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| author | Shivamoggi, Bhimsen K. |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0047-5 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781461200475 9781461265887 |
| language | English |
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| spelling | Shivamoggi, Bhimsen K. Verfasser aut Perturbation Methods for Differential Equations by Bhimsen K. Shivamoggi Boston, MA Birkhäuser Boston 2003 1 Online-Ressource (XIV, 354 p) txt rdacontent c rdamedia cr rdacarrier In nonlinear problems, essentially new phenomena occur which have no place in the corresponding linear problems. Therefore, in the study of nonlinear problems the major purpose is not so much to introduce methods that improve the accuracy of linear methods, but to focus attention on those features of the nonlinearities that result in distinctively new phenomena. Among the latter are - * existence of solutions ofperiodic problems for all frequencies rather than only a setofcharacteristic values, * dependenceofamplitude on frequency, * removal ofresonance infinities, * appearance ofjump phenomena, * onsetofchaotic motions. On the other hand, mathematical problems associated with nonlinearities are so complex that a comprehensive theory of nonlinear phenomena is out of the question.' Consequently, one practical approach is to settle for something less than complete generality. Thus, one gives up the study of global behavior of solutions of a nonlinear problem and seeks nonlinear solutions in the neighborhood of (or as perturbations about) a known linear solution. This is the basic idea behind a perturbative solutionofa nonlinear problem Mathematics Differential Equations Computer science / Mathematics Engineering Ordinary Differential Equations Computational Mathematics and Numerical Analysis Applications of Mathematics Computational Intelligence Informatik Ingenieurwissenschaften Mathematik Störungstheorie (DE-588)4128420-3 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Störungstheorie (DE-588)4128420-3 s 1\p DE-604 https://doi.org/10.1007/978-1-4612-0047-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Shivamoggi, Bhimsen K. Perturbation Methods for Differential Equations Mathematics Differential Equations Computer science / Mathematics Engineering Ordinary Differential Equations Computational Mathematics and Numerical Analysis Applications of Mathematics Computational Intelligence Informatik Ingenieurwissenschaften Mathematik Störungstheorie (DE-588)4128420-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4128420-3 (DE-588)4012249-9 |
| title | Perturbation Methods for Differential Equations |
| title_auth | Perturbation Methods for Differential Equations |
| title_exact_search | Perturbation Methods for Differential Equations |
| title_full | Perturbation Methods for Differential Equations by Bhimsen K. Shivamoggi |
| title_fullStr | Perturbation Methods for Differential Equations by Bhimsen K. Shivamoggi |
| title_full_unstemmed | Perturbation Methods for Differential Equations by Bhimsen K. Shivamoggi |
| title_short | Perturbation Methods for Differential Equations |
| title_sort | perturbation methods for differential equations |
| topic | Mathematics Differential Equations Computer science / Mathematics Engineering Ordinary Differential Equations Computational Mathematics and Numerical Analysis Applications of Mathematics Computational Intelligence Informatik Ingenieurwissenschaften Mathematik Störungstheorie (DE-588)4128420-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Mathematics Differential Equations Computer science / Mathematics Engineering Ordinary Differential Equations Computational Mathematics and Numerical Analysis Applications of Mathematics Computational Intelligence Informatik Ingenieurwissenschaften Mathematik Störungstheorie Differentialgleichung |
| url | https://doi.org/10.1007/978-1-4612-0047-5 |
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