Global error estimation for stiff differential equations: globale Fehlerschätzung für steife Differentialgleichungen
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
München
Dr. Hut
2017
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| Ausgabe: | 1. Auflage |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | viii, 95 Seiten 21 cm x 14.8 cm, 173 g |
| ISBN: | 9783843931342 3843931348 |
Internformat
MARC
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| 245 | 1 | 0 | |a Global error estimation for stiff differential equations |b globale Fehlerschätzung für steife Differentialgleichungen |c von Dipl.-Math. Alexander Rath aus Wiesbaden |
| 250 | |a 1. Auflage | ||
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| 502 | |b Dissertation |c Technische Universität Darmstadt |d 2016 | ||
| 653 | |a global error estimation | ||
| 653 | |a asymptotic correctness | ||
| 653 | |a discrete approximations | ||
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Datensatz im Suchindex
| _version_ | 1806413680282173440 |
|---|---|
| adam_text |
Global Error Estimation for
Stiff Differential Equations
Globale Fehlerschätzung für steife Differentialgleichungen
Zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr rer nat )
genehmigte Dissertation von Dipl -Math Alexander Daniel Rath aus
Wiesbaden
2017-Darmstadt-D 17
TECHNISCHE
UNIVERSITÄT
DARMSTADT
Fachbereich Mathematik
Forschungsbereich Numerik und
Wissenschaftliches Rechnen
Contents
1 Introduction 1
2 Theory of stiff differential equations 5
2 1 Characterization of stiff problems 5
2 2 One-sided Lipschitz constants 5
2 3 Stability concepts 8
2 4 B-convergence 12
3 Characteristics of the implicit midpoint rule 15
3 1 Stability properties 16
3 2 Consistency and B-convergence 19
4 Error estimation 23
4 1 The general setting 23
4 2 Solving hard problems 25
4 3 Tolerance proportionality 26
431 Error per unit step 27
432 Error per step 28
4 4 General strategies for global error estimation 29
441 Error estimation using two methods 29
442 Error estimation via extrapolation 31
443 The adjoint approach 31
444 Solving the error equation 33
4 5 Error estimation for stiff ODEs 34
4 6 Solving the error equation for stiff systems 35
461 Linear extension 36
462 Piecewise cubic Hermite interpolation 38
5 Proof of asymptotic correctness of the error estimator 41
5 1 Preliminaries 41
5 2 Linear Extension 46
521 Linear problems 47
522 Nonlinear, autonomous problems 49
523 General nonlinear problems 53
vii
5 3 Hermite extension 58
531 Preliminaries 58
532 The scheme and propagation of perturbations 62
533 Convergence and asymptotic correctness 63
6 Numerical Results 67
6 1 Heat equation with Dirichlet boundary conditions 68
6 2 Damped wave equation 73
6 3 Brusselator 77
6 4 FitzHugh amp; Nagumo equation 81
7 Conclusion 85
Nomenclature 87
Bibliography 89
Lebenslauf 95 |
| any_adam_object | 1 |
| author | Rath, Alexander 1984- |
| author_GND | (DE-588)1133587976 |
| author_facet | Rath, Alexander 1984- |
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| bvnumber | BV044341568 |
| ctrlnum | (OCoLC)992495370 (DE-599)DNB1133030726 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Auflage |
| format | Thesis Book |
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| spelling | Rath, Alexander 1984- Verfasser (DE-588)1133587976 aut Global error estimation for stiff differential equations globale Fehlerschätzung für steife Differentialgleichungen von Dipl.-Math. Alexander Rath aus Wiesbaden 1. Auflage München Dr. Hut 2017 viii, 95 Seiten 21 cm x 14.8 cm, 173 g txt rdacontent n rdamedia nc rdacarrier Dissertation Technische Universität Darmstadt 2016 global error estimation asymptotic correctness discrete approximations (DE-588)4113937-9 Hochschulschrift gnd-content Verlag Dr. Hut (München) (DE-588)10174118-2 pbl X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=f3d4eca7041a4828a6938b4379a92cef&prov=M&dok_var=1&dok_ext=htm Inhaltstext HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029744593&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rath, Alexander 1984- Global error estimation for stiff differential equations globale Fehlerschätzung für steife Differentialgleichungen |
| subject_GND | (DE-588)4113937-9 |
| title | Global error estimation for stiff differential equations globale Fehlerschätzung für steife Differentialgleichungen |
| title_auth | Global error estimation for stiff differential equations globale Fehlerschätzung für steife Differentialgleichungen |
| title_exact_search | Global error estimation for stiff differential equations globale Fehlerschätzung für steife Differentialgleichungen |
| title_full | Global error estimation for stiff differential equations globale Fehlerschätzung für steife Differentialgleichungen von Dipl.-Math. Alexander Rath aus Wiesbaden |
| title_fullStr | Global error estimation for stiff differential equations globale Fehlerschätzung für steife Differentialgleichungen von Dipl.-Math. Alexander Rath aus Wiesbaden |
| title_full_unstemmed | Global error estimation for stiff differential equations globale Fehlerschätzung für steife Differentialgleichungen von Dipl.-Math. Alexander Rath aus Wiesbaden |
| title_short | Global error estimation for stiff differential equations |
| title_sort | global error estimation for stiff differential equations globale fehlerschatzung fur steife differentialgleichungen |
| title_sub | globale Fehlerschätzung für steife Differentialgleichungen |
| topic_facet | Hochschulschrift |
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