The numerical solution of differential-algebraic systems by Runge-Kutta methods:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1989
|
| Schriftenreihe: | Lecture notes in mathematics
1409 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 133 - 137 |
| Beschreibung: | VII, 139 S. graph. Darst. |
| ISBN: | 3540518606 0387518606 |
Internformat
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| 100 | 1 | |a Hairer, Ernst |d 1949- |e Verfasser |0 (DE-588)139445188 |4 aut | |
| 245 | 1 | 0 | |a The numerical solution of differential-algebraic systems by Runge-Kutta methods |c Ernst Hairer ; Christian Lubich ; Michel Roche |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1989 | |
| 300 | |a VII, 139 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1409 | |
| 500 | |a Literaturverz. S. 133 - 137 | ||
| 650 | 7 | |a Gewone differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Numerieke methoden |2 gtt | |
| 650 | 4 | |a Runge-Kutta, Méthode de | |
| 650 | 4 | |a Équations différentielles algébriques - Solutions numériques | |
| 650 | 4 | |a Differential-algebraic equations |x Numerical solutions | |
| 650 | 4 | |a Runge-Kutta formulas | |
| 650 | 0 | 7 | |a Differential-algebraisches Gleichungssystem |0 (DE-588)4229517-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Runge-Kutta-Verfahren |0 (DE-588)4203408-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differential-algebraisches Gleichungssystem |0 (DE-588)4229517-8 |D s |
| 689 | 0 | 1 | |a Runge-Kutta-Verfahren |0 (DE-588)4203408-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Lubich, Christian |d 1959- |e Verfasser |0 (DE-588)11167090X |4 aut | |
| 700 | 1 | |a Roché, Michel |e Verfasser |4 aut | |
| 830 | 0 | |a Lecture notes in mathematics |v 1409 |w (DE-604)BV000676446 |9 1409 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001585635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Datensatz im Suchindex
| _version_ | 1805082659342254080 |
|---|---|
| adam_text |
Contents
1. Description of differential-algebraic problems 1
Index of a differential-algebraic system 1
Systems of index 1 2
Systems of index 2 3
Systems of index 3 7
The pendulum 8
Singularly perturbed problems 9
Singular singularly perturbed problems 10
Other definitions of the index 12
Notes 13
2. Runge-Kutta methods for differential-algebraic equations 14
Runge-Kutta methods for ordinary differential equations 14
Extension to differential-algebraic problems 14
Classes of implicit Runge-Kutta methods 15
Summary of convergence results 17
Singularly perturbed problems 19
Half-explicit methods 20
An index 2 example where numerical methods fail 21
3. Convergence for index 1 problems 23
Solving the equivalent ordinary differential equation 23
The direct approach 24
Convergence 25
Asymptotic expansion of the global error 27
Notes 28
4. Convergence for index 2 problems 30
Existence and uniqueness of Runge-Kutta solution 31
Influence of perturbations 33
The local error 34
Convergence for the y-component 36
Convergence for the ^-component 40
Perturbed asymptotic expansion 40
Convergence for R(oo) — ±1 45
Convergence for Lobatto IIIA methods 46
Verification of Table 2.3 47
Convergence of half-explicit methods 48
VI
/^-extrapolation of the half-explicit midpoint rule 50
Notes 54
5. Order conditions of Runge-Kutta methods for index 2 systems 55
Taylor expansion of the exact solution 55
Taylor expansion of the numerical solution 59
Order conditions 62
Simplifying assumptions 64
Order conditions for half-explicit methods 68
Notes 70
6. Convergence for index 3 problems 71
Existence and uniqueness of Runge-Kutta solution 72
Influence of perturbations 75
The local error 76
Preliminary convergence result 78
Perturbed asymptotic expansions 82
Higher order convergence for the y-component 86
A half-explicit extrapolation method 90
Notes 91
7. Solution of nonlinear systems by simplified Newton 92
Index 1 92
Index 2 93
Index 3 95
Problems B(y)yr = a(y) 96
Scaling of linear systems 97
Notes 98
8. Local error estimation 99
Index 1 99
Index 2 100
Index 3 103
Notes 105
9. Examples of differential-algebraic systems and their solution . 106
Two phase plug flow problem 106
Two transistor amplifier 108
Ring modulator 112
Discharge pressure control 116
Pendulum 118
VII
Stiff spring pendulum 119
Van der Pol equation 121
Notes 123
10. Appendix: The code RADAU5 124
Driver example for the pendulum 124
The subroutine RADAU5 127
Bibliography 133
Subject index 138 |
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| dewey-raw | 510 515/.352 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002448060 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:36:10Z |
| institution | BVB |
| isbn | 3540518606 0387518606 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001585635 |
| oclc_num | 603635211 |
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| physical | VII, 139 S. graph. Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Hairer, Ernst 1949- Verfasser (DE-588)139445188 aut The numerical solution of differential-algebraic systems by Runge-Kutta methods Ernst Hairer ; Christian Lubich ; Michel Roche Berlin [u.a.] Springer 1989 VII, 139 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1409 Literaturverz. S. 133 - 137 Gewone differentiaalvergelijkingen gtt Numerieke methoden gtt Runge-Kutta, Méthode de Équations différentielles algébriques - Solutions numériques Differential-algebraic equations Numerical solutions Runge-Kutta formulas Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd rswk-swf Runge-Kutta-Verfahren (DE-588)4203408-5 gnd rswk-swf Differential-algebraisches Gleichungssystem (DE-588)4229517-8 s Runge-Kutta-Verfahren (DE-588)4203408-5 s DE-604 Lubich, Christian 1959- Verfasser (DE-588)11167090X aut Roché, Michel Verfasser aut Lecture notes in mathematics 1409 (DE-604)BV000676446 1409 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001585635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hairer, Ernst 1949- Lubich, Christian 1959- Roché, Michel The numerical solution of differential-algebraic systems by Runge-Kutta methods Lecture notes in mathematics Gewone differentiaalvergelijkingen gtt Numerieke methoden gtt Runge-Kutta, Méthode de Équations différentielles algébriques - Solutions numériques Differential-algebraic equations Numerical solutions Runge-Kutta formulas Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Runge-Kutta-Verfahren (DE-588)4203408-5 gnd |
| subject_GND | (DE-588)4229517-8 (DE-588)4203408-5 |
| title | The numerical solution of differential-algebraic systems by Runge-Kutta methods |
| title_auth | The numerical solution of differential-algebraic systems by Runge-Kutta methods |
| title_exact_search | The numerical solution of differential-algebraic systems by Runge-Kutta methods |
| title_full | The numerical solution of differential-algebraic systems by Runge-Kutta methods Ernst Hairer ; Christian Lubich ; Michel Roche |
| title_fullStr | The numerical solution of differential-algebraic systems by Runge-Kutta methods Ernst Hairer ; Christian Lubich ; Michel Roche |
| title_full_unstemmed | The numerical solution of differential-algebraic systems by Runge-Kutta methods Ernst Hairer ; Christian Lubich ; Michel Roche |
| title_short | The numerical solution of differential-algebraic systems by Runge-Kutta methods |
| title_sort | the numerical solution of differential algebraic systems by runge kutta methods |
| topic | Gewone differentiaalvergelijkingen gtt Numerieke methoden gtt Runge-Kutta, Méthode de Équations différentielles algébriques - Solutions numériques Differential-algebraic equations Numerical solutions Runge-Kutta formulas Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Runge-Kutta-Verfahren (DE-588)4203408-5 gnd |
| topic_facet | Gewone differentiaalvergelijkingen Numerieke methoden Runge-Kutta, Méthode de Équations différentielles algébriques - Solutions numériques Differential-algebraic equations Numerical solutions Runge-Kutta formulas Differential-algebraisches Gleichungssystem Runge-Kutta-Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001585635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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