Validated computation of connecting orbits in ordinary differential equations:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2013
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| Schlagworte: | |
| Online-Zugang: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130701-1141240-0-8 Inhaltsverzeichnis |
| Beschreibung: | 152 S. graph. Darst. |
Internformat
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| 245 | 1 | 0 | |a Validated computation of connecting orbits in ordinary differential equations |c Christian P. Reinhardt |
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Datensatz im Suchindex
| _version_ | 1804150619043266560 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 9
2 BACKGROUND 19
2.1 DYNAMICAL SYSTEMS 19
2.1.1 BASIC DEFINITIONS FROM DYNAMICAL SYSTEMS THEORY . . 19 2.1.2 THE
PARAMETRIZATION METHOD 24
2.2 SPLINE AND SPECTRAL APPROXIMATION 36
2.2.1 SPECTRAL APPROXIMATION 36
3 RIGOROUS NUMERICS FOR CONNECTING ORBITS 45
3.1 DISCRETIZATION FREE APPROACH 46
3.1.1 GENERAL VALIDATION METHOD USING NEWTON-KANTOROVICH 46 3.1.2
VALIDATION OF CONNECTING ORBITS 49
3.2 APPROACH SOLVING A BOUNDARY VALUE PROBLEM 56
3.2.1 VALIDATION OF CONNECTING ORBITS: SPLINE APPROACH . . 60 3.2.2
VALIDATION OF CONNECTING ORBITS: CHEBYSHEV APPROACH 64 3.3 RESULTS ON
TRANSVERSALITY 74
3.3.1 DISCRETIZATION FREE APPROACH 75
3.3.2 SPLINE APPROACH 77
3.3.3 CHEBYSHEV APPROACH 80
4 APPLICATIONS AND APPROACH COMPARISON 83
4.1 SYMMETRIC CONNECTIONS IN THE GRAY SCOTT SYSTEM 84
4.1.1 BACKGROUND ON THE GRAY-SCOTT SYSTEM AND RESULTS . . 84 4.1.2
FORMULATION OF THE OPERATOR AND CONSTRUCTION OF THE RADII POLYNOMIAL
BOUNDS FOR THE CHEBYSHEV APPROACH 89 4.2 THE LORENZ SYSTEM 108
4.2.1 DISCRETIZATION-FREE APPROACH 109
4.2.2 RIGOROUS SOLUTIONS OF IVPS 119
4.2.3 CONNECTIONS USING THE BOUNDARY VALUE APPROACH . . 140
3
HTTP://D-NB.INFO/1042542317
IMAGE 2
CONTENTS
CONCLUSION 145
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| any_adam_object | 1 |
| author | Reinhardt, Christian |
| author_facet | Reinhardt, Christian |
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| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-07-10T00:41:48Z |
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| language | English |
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| spelling | Reinhardt, Christian Verfasser aut Validated computation of connecting orbits in ordinary differential equations Christian P. Reinhardt 2013 152 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2013 Dynamisches System (DE-588)4013396-5 gnd rswk-swf Orbit Mathematik (DE-588)4238277-4 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Dynamisches System (DE-588)4013396-5 s Orbit Mathematik (DE-588)4238277-4 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20130701-1141240-0-8 http://mediatum.ub.tum.de/node?id=1141240 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130701-1141240-0-8 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026170632&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reinhardt, Christian Validated computation of connecting orbits in ordinary differential equations Dynamisches System (DE-588)4013396-5 gnd Orbit Mathematik (DE-588)4238277-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4238277-4 (DE-588)4128130-5 (DE-588)4113937-9 |
| title | Validated computation of connecting orbits in ordinary differential equations |
| title_auth | Validated computation of connecting orbits in ordinary differential equations |
| title_exact_search | Validated computation of connecting orbits in ordinary differential equations |
| title_full | Validated computation of connecting orbits in ordinary differential equations Christian P. Reinhardt |
| title_fullStr | Validated computation of connecting orbits in ordinary differential equations Christian P. Reinhardt |
| title_full_unstemmed | Validated computation of connecting orbits in ordinary differential equations Christian P. Reinhardt |
| title_short | Validated computation of connecting orbits in ordinary differential equations |
| title_sort | validated computation of connecting orbits in ordinary differential equations |
| topic | Dynamisches System (DE-588)4013396-5 gnd Orbit Mathematik (DE-588)4238277-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Dynamisches System Orbit Mathematik Numerisches Verfahren Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1141240 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130701-1141240-0-8 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026170632&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT reinhardtchristian validatedcomputationofconnectingorbitsinordinarydifferentialequations |