Numerical methods for ordinary differential systems: the initial value problem
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester u.a.
Wiley
1991
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 293 S. graph. Darst. |
| ISBN: | 0471929905 |
Internformat
MARC
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| 100 | 1 | |a Lambert, John D. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical methods for ordinary differential systems |b the initial value problem |c J. D. Lambert |
| 264 | 1 | |a Chichester u.a. |b Wiley |c 1991 | |
| 300 | |a X, 293 S. |b graph. Darst. | ||
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| 650 | 7 | |a Gewone differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Numerieke methoden |2 gtt | |
| 650 | 4 | |a Initial value problems |x Numerical solutions | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface ix
1 Background Material 1
1.1 Introduction 1
1.2 Notation 1
1.3 Mean value theorems 2
1.4 First order systems of ordinary differential equations 4
1.5 Higher order systems 6
1.6 Linear systems with constant coefficients 8
1.7 Systems of linear difference equations with constant coefficients 9
1.8 Iterative methods for nonlinear systems of algebraic equations 11
1.9 Schur polynomials 13
1.10 Interpolation formulae 15
1.11 The direct product of matrices 19
2 Introduction to Numerical Methods 21
2.1 The role of numerical methods for initial value problems 21
2.2 Numerical methods; nomenclature and examples 22
2.3 Convergence 25
2.4 Consistency 27
2.5 Zero stability 31
2.6 The syntax of a stability definition 37
2.7 Some numerical experiments 39
3 Linear Multistep Methods 45
3.1 Notation and nomenclature 45
3.2 The associated difference operator; order and error constant 47
3.3 The link with polynomial interpolation 52
3.4 The first Dahlquist barrier 55
3.5 Local truncation error and global truncation error 56
3.6 Error bounds 59
3.7 Local error 62
3.8 Linear stability theory 68
3.9 Adams methods in backward difference form 80
3.10 Properties of the Adams coefficients 87
3.11 General linear multistep methods in backward difference form 91
3.12 The backward differentiation formulae 98
4 Predictor Corrector Methods 103
4.1 Predictor—corrector modes 103
4.2 The local truncation error of predictor corrector methods 105
4.3 Milne s estimate for the PLTE; local extrapolation 107
4.4 Predictor corrector methods based on Adams methods in backward difference form 110
4.5 Predictor corrector methods based on general linear multistep methods in backward difference form 115
4.6 Linear stability theory for predictor corrector methods 117
viii CONTENTS
4.7 Changing the steplength in an ABM algorithm 128
4.8 Changing the steplength; doubling and halving 129
4.9 Changing the steplength; the Nordsieck vector and Gear s implementation 132
4.10 Changing the steplength; variable coefficient techniques 138
4.11 The structure of VSVO algorithms 143
5 Runge Kutta Methods 149
5.1 Introduction 149
5.2 Consistency, local truncation error, order and convergence 151
5.3 Derivation of explicit Runge Kutta methods for scalar problems 153
5.4 The Butcher theory; introduction 157
5.5 The Afth Frechet derivative; elementary differentials 158
5.6 Rooted trees 162
5.7 Order conditions 165
5.8 Scalar problems and systems 173
5.9 Explicit methods; attainable order 176
5.10 Explicit methods; local error estimation 182
5.11 Implicit and semi implicit methods 189
5.12 Linear stability theory for Runge Kutta methods 198
5.13 Order conditions; the alternative approach of Albrecht 205
6 Stiffness: Linear Stability Theory 213
6.1. A preliminary numerical experiment 213
6.2 The nature of stiffness 216
6.3 Linear stability definitions pertinent to stiffness 224
6.4 Rational approximations to the exponential; order stars 232
6.5 Handling implicitness in the context of stiffness 237
6.6 Linear multistep methods for stiff systems 243
6.7 Runge Kutta methods for stiff systems 247
6.8 Methods involving the Jacobian 251
6.9 Correlation with finite difference methods for partial differential equations 254
7 Stiffness: Nonlinear Stability Theory 261
7.1 The shortcomings of linear stability theory 261
7.2 Contractivity 265
7.3 The one sided Lipschitz constant and the logarithmic norm 266
7.4 6 stability 271
7.5 Nonlinear stability of implicit Runge Kutta methods 273
7.6 ^ convergence 280
7.7 Conclusions 283
References 28S
Index 291
|
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| id | DE-604.BV004636389 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:15:20Z |
| institution | BVB |
| isbn | 0471929905 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002846119 |
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| physical | X, 293 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Wiley |
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| spelling | Lambert, John D. Verfasser aut Numerical methods for ordinary differential systems the initial value problem J. D. Lambert Chichester u.a. Wiley 1991 X, 293 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Equacoes diferenciais larpcal Gewone differentiaalvergelijkingen gtt Numerieke methoden gtt Initial value problems Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002846119&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lambert, John D. Numerical methods for ordinary differential systems the initial value problem Equacoes diferenciais larpcal Gewone differentiaalvergelijkingen gtt Numerieke methoden gtt Initial value problems Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4020929-5 |
| title | Numerical methods for ordinary differential systems the initial value problem |
| title_auth | Numerical methods for ordinary differential systems the initial value problem |
| title_exact_search | Numerical methods for ordinary differential systems the initial value problem |
| title_full | Numerical methods for ordinary differential systems the initial value problem J. D. Lambert |
| title_fullStr | Numerical methods for ordinary differential systems the initial value problem J. D. Lambert |
| title_full_unstemmed | Numerical methods for ordinary differential systems the initial value problem J. D. Lambert |
| title_short | Numerical methods for ordinary differential systems |
| title_sort | numerical methods for ordinary differential systems the initial value problem |
| title_sub | the initial value problem |
| topic | Equacoes diferenciais larpcal Gewone differentiaalvergelijkingen gtt Numerieke methoden gtt Initial value problems Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Equacoes diferenciais Gewone differentiaalvergelijkingen Numerieke methoden Initial value problems Numerical solutions Numerisches Verfahren Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002846119&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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