Differential-algebraic equations analysis and numerical solution
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Zürich
European Math. Soc.
2006
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| Schriftenreihe: | EMS textbooks in mathematics
|
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| Online-Zugang: | Inhaltsverzeichnis |
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MARC
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| 100 | 1 | |a Kunkel, Peter |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differential-algebraic equations |b analysis and numerical solution |c Peter Kunkel ; Volker Mehrmann |
| 246 | 1 | 3 | |a Differential algebraic equations |
| 264 | 1 | |a Zürich |b European Math. Soc. |c 2006 | |
| 300 | |a VIII, 377 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a EMS textbooks in mathematics | |
| 650 | 4 | |a Problèmes aux limites | |
| 650 | 4 | |a Équations différentielles algébriques | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Differential-algebraic equations | |
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| 650 | 0 | 7 | |a Differential-algebraisches Gleichungssystem |0 (DE-588)4229517-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Mehrmann, Volker |e Verfasser |4 aut | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-014712081 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0041/MAT 340f 2014 A 1803 |
|---|---|
| DE-BY-TUM_katkey | 1988282 |
| DE-BY-TUM_media_number | 040008355171 |
| _version_ | 1816713933847789568 |
| adam_text |
Contents
I Analysis of differential-algebraic equations
1
1
Introduction
3
1.1
Solvability concepts
. 5
1.2
Index concepts
. 6
1.3
Applications
. 8
1.4
How to use this book in teaching
. 11
2
Linear differential-algebraic equations with constant coefficients
13
2.1
Canonical forms
. 13
2.2
The Drazin inverse
. 22
2.3
Explicit representation of solutions
. 27
2.4
Generalized solutions
. 32
2.5
Control problems
. 48
Bibliographical remarks
. 52
Exercises
. 53
3
Linear differential-algebraic equations with variable coefficients
56
3.1
Canonical forms
. 56
3.2
Local and global invariants
. 80
3.3
The differentiation index
. 96
3.4
Differential-algebraic operators and generalized inverses
. 114
3.5
Generalized solutions
. 132
3.6
Control problems
. 138
Bibliographical remarks
. 147
Exercises
. 147
4
Nonlinear differential-algebraic equations
151
4.1
Existence and uniqueness of solutions
. 151
4.2
Structured problems
. 167
4.3
Over-and underdetermined problems
. 182
4.4
Control problems
. 189
4.5
Differential equations on manifolds
. 195
Bibliographical remarks
. 210
Exercises
. 210
viii Contents
II Numerical solution of differential-algebraic equations
215
5
Numerical methods for strangeness-free problems
217
5.1
Preparations
. 218
5.2
One-step methods
. 224
5.3
Multi-step methods
. 254
Bibliographical remarks
. 270
Exercises
. 270
6
Numerical methods for index reduction
273
6.1
Index reduction for linear problems
. 274
6.2
Index reduction for nonlinear problems
. 279
6.3
Index reduction via feedback control
. 284
6.4
Index reduction by minimal extension
. 286
Bibliographical remarks
. 295
Exercises
. 295
7
Boundary value problems
298
7.1
Existence and uniqueness of solutions
. 299
7.2
Multiple shooting
. 304
7.3
Collocation
. 314
Bibliographical remarks
. 348
Exercises
. 348
8
Software for the numerical solution of differential-algebraic
equations
352
Bibliographical remarks
. 355
Exercises
. 355
Final remarks
357
Bibliography
359
Index
373 |
| adam_txt |
Contents
I Analysis of differential-algebraic equations
1
1
Introduction
3
1.1
Solvability concepts
. 5
1.2
Index concepts
. 6
1.3
Applications
. 8
1.4
How to use this book in teaching
. 11
2
Linear differential-algebraic equations with constant coefficients
13
2.1
Canonical forms
. 13
2.2
The Drazin inverse
. 22
2.3
Explicit representation of solutions
. 27
2.4
Generalized solutions
. 32
2.5
Control problems
. 48
Bibliographical remarks
. 52
Exercises
. 53
3
Linear differential-algebraic equations with variable coefficients
56
3.1
Canonical forms
. 56
3.2
Local and global invariants
. 80
3.3
The differentiation index
. 96
3.4
Differential-algebraic operators and generalized inverses
. 114
3.5
Generalized solutions
. 132
3.6
Control problems
. 138
Bibliographical remarks
. 147
Exercises
. 147
4
Nonlinear differential-algebraic equations
151
4.1
Existence and uniqueness of solutions
. 151
4.2
Structured problems
. 167
4.3
Over-and underdetermined problems
. 182
4.4
Control problems
. 189
4.5
Differential equations on manifolds
. 195
Bibliographical remarks
. 210
Exercises
. 210
viii Contents
II Numerical solution of differential-algebraic equations
215
5
Numerical methods for strangeness-free problems
217
5.1
Preparations
. 218
5.2
One-step methods
. 224
5.3
Multi-step methods
. 254
Bibliographical remarks
. 270
Exercises
. 270
6
Numerical methods for index reduction
273
6.1
Index reduction for linear problems
. 274
6.2
Index reduction for nonlinear problems
. 279
6.3
Index reduction via feedback control
. 284
6.4
Index reduction by minimal extension
. 286
Bibliographical remarks
. 295
Exercises
. 295
7
Boundary value problems
298
7.1
Existence and uniqueness of solutions
. 299
7.2
Multiple shooting
. 304
7.3
Collocation
. 314
Bibliographical remarks
. 348
Exercises
. 348
8
Software for the numerical solution of differential-algebraic
equations
352
Bibliographical remarks
. 355
Exercises
. 355
Final remarks
357
Bibliography
359
Index
373 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T14:13:47Z |
| indexdate | 2024-11-25T17:37:10Z |
| institution | BVB |
| isbn | 3037190175 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014712081 |
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| physical | VIII, 377 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
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| publisher | European Math. Soc. |
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| series2 | EMS textbooks in mathematics |
| spellingShingle | Kunkel, Peter Mehrmann, Volker Differential-algebraic equations analysis and numerical solution Problèmes aux limites Équations différentielles algébriques Boundary value problems Differential-algebraic equations Dynamisches System (DE-588)4013396-5 gnd Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4229517-8 (DE-588)4128130-5 |
| title | Differential-algebraic equations analysis and numerical solution |
| title_alt | Differential algebraic equations |
| title_auth | Differential-algebraic equations analysis and numerical solution |
| title_exact_search | Differential-algebraic equations analysis and numerical solution |
| title_exact_search_txtP | Differential-algebraic equations analysis and numerical solution |
| title_full | Differential-algebraic equations analysis and numerical solution Peter Kunkel ; Volker Mehrmann |
| title_fullStr | Differential-algebraic equations analysis and numerical solution Peter Kunkel ; Volker Mehrmann |
| title_full_unstemmed | Differential-algebraic equations analysis and numerical solution Peter Kunkel ; Volker Mehrmann |
| title_short | Differential-algebraic equations |
| title_sort | differential algebraic equations analysis and numerical solution |
| title_sub | analysis and numerical solution |
| topic | Problèmes aux limites Équations différentielles algébriques Boundary value problems Differential-algebraic equations Dynamisches System (DE-588)4013396-5 gnd Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Problèmes aux limites Équations différentielles algébriques Boundary value problems Differential-algebraic equations Dynamisches System Differential-algebraisches Gleichungssystem Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014712081&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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