Generalized Wiener expansions for the numerical solution of random ordinary differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
München
Verl. Dr. Hut
2012
|
| Ausgabe: | 1. Aufl. |
| Schriftenreihe: | Mathematik
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | V, 111 S. graph. Darst. 210 mm x 148 mm, 186 g |
| ISBN: | 9783843903202 3843903204 |
Internformat
MARC
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| 245 | 1 | 0 | |a Generalized Wiener expansions for the numerical solution of random ordinary differential equations |c Florian Markus Augustin |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a München |b Verl. Dr. Hut |c 2012 | |
| 300 | |a V, 111 S. |b graph. Darst. |c 210 mm x 148 mm, 186 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Mathematik | |
| 502 | |a Zugl.: München, Techn. Univ., Diss., 2011 | ||
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Datensatz im Suchindex
| _version_ | 1804148870410665984 |
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| adam_text | IMAGE 1
CONTENTS
1. INTRODUCTION 1
2. T H E WIENER T E R M S O F CHAOS 5
2.1. BASIC CONCEPTS OF PROBABILITY THEORY 5
2.2. GAUSSIAN HILBERT SPACES AND HOMOGENEOUS CHAOS 6
2.3. GENERALIZED WIENER EXPANSIONS 9
2.4. COMPUTATION OF STATISTICAL QUANTITIES 11
2.5. THE KARHUNEN-LOEVE EXPANSION 12
3. WIENER M E T H O D S FOR RANDOM ORDINARY DIFFERENTIAL EQUATIONS 15
3.1. RANDOM ORDINARY DIFFERENTIAL EQUATIONS (RODES) 15
3.2. THE STOCHASTIC COLLOCATION METHODS . 16
3.3. THE STOCHASTIC GALERKIN METHOD 18
3.4. THE MULTI-ELEMENT GENERALIZED POLYNOMIAL CHAOS APPROACH 20
4. STOCHASTIC GALERKIN RUNGE K U T T A M E T H O D S 2 3
4.1. TRUNCATION ERROR OF THE PROJECTED WIENER EXPANSION 24
4.2. LOCAL DISCRETIZATION ERROR AND CONSISTENCY 30
4.3. ASYMPTOTIC BOUND OF THE GLOBAL ERROR 35
4.4. CONVERGENCE OF THE MULTI-ELEMENT APPROACH 41
4.5. STABILITY OF THE PROJECTED SYSTEM 42
5. T H E INTEGRATOR ARODE 5 1
5.1. AUTOMATIC GENERATION OF THE PROJECTED SYSTEM 51
5.2. MESH REFINEMENT AND COARSENING 54
5.3. ERROR ESTIMATORS FOR TIME AND MESH ADAPTIVITY 57
5.4. THE ALGORITHM ARODE 59
6. NUMERICAL SIMULATIONS 6 1
6.1. RODES WITH STEADY DISTRIBUTION 62
6.2. RODES WITH UNSTEADY DISTRIBUTION 67
6.3. RODES WITH STEEP GRADIENTS IN PARAMETER SPACE 88
7. CONCLUSIONS 1 0 1
A. RUNGE-KUTTA M E T H O D S 1 0 3
B. AUXILIARY THEOREMS 105
HTTP://D-NB.INFO/1019448644
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| any_adam_object | 1 |
| author | Augustin, Florian |
| author_facet | Augustin, Florian |
| author_role | aut |
| author_sort | Augustin, Florian |
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| building | Verbundindex |
| bvnumber | BV039913297 |
| ctrlnum | (OCoLC)780132747 (DE-599)DNB1019448644 |
| dewey-full | 519.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.22 |
| dewey-search | 519.22 |
| dewey-sort | 3519.22 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Thesis Book |
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| id | DE-604.BV039913297 |
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| indexdate | 2024-07-10T00:14:00Z |
| institution | BVB |
| isbn | 9783843903202 3843903204 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024771921 |
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| physical | V, 111 S. graph. Darst. 210 mm x 148 mm, 186 g |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Verl. Dr. Hut |
| record_format | marc |
| series2 | Mathematik |
| spelling | Augustin, Florian Verfasser aut Generalized Wiener expansions for the numerical solution of random ordinary differential equations Florian Markus Augustin 1. Aufl. München Verl. Dr. Hut 2012 V, 111 S. graph. Darst. 210 mm x 148 mm, 186 g txt rdacontent n rdamedia nc rdacarrier Mathematik Zugl.: München, Techn. Univ., Diss., 2011 Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Hermitesche Entwicklung (DE-588)4651193-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Stochastische Differentialgleichung (DE-588)4057621-8 s Numerisches Verfahren (DE-588)4128130-5 s Hermitesche Entwicklung (DE-588)4651193-3 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024771921&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Augustin, Florian Generalized Wiener expansions for the numerical solution of random ordinary differential equations Numerisches Verfahren (DE-588)4128130-5 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Hermitesche Entwicklung (DE-588)4651193-3 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4057621-8 (DE-588)4651193-3 (DE-588)4113937-9 |
| title | Generalized Wiener expansions for the numerical solution of random ordinary differential equations |
| title_auth | Generalized Wiener expansions for the numerical solution of random ordinary differential equations |
| title_exact_search | Generalized Wiener expansions for the numerical solution of random ordinary differential equations |
| title_full | Generalized Wiener expansions for the numerical solution of random ordinary differential equations Florian Markus Augustin |
| title_fullStr | Generalized Wiener expansions for the numerical solution of random ordinary differential equations Florian Markus Augustin |
| title_full_unstemmed | Generalized Wiener expansions for the numerical solution of random ordinary differential equations Florian Markus Augustin |
| title_short | Generalized Wiener expansions for the numerical solution of random ordinary differential equations |
| title_sort | generalized wiener expansions for the numerical solution of random ordinary differential equations |
| topic | Numerisches Verfahren (DE-588)4128130-5 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Hermitesche Entwicklung (DE-588)4651193-3 gnd |
| topic_facet | Numerisches Verfahren Stochastische Differentialgleichung Hermitesche Entwicklung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024771921&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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