Numerical methods for partial differential equations
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| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Academic Press [u.a.]
1977
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Applications of mathematics series.
Computer science and applied mathematics |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Academic Press [u.a.] |c 1977 | |
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Datensatz im Suchindex
| _version_ | 1819685943058104320 |
|---|---|
| adam_text | Contents
Preface to second edition xi
Preface to first edition xiii
1 Fundamentals
1 0 Introduction 1
1 1 Classification of physical problems 3
1 2 Classification of equations 5
1 3 Asymptotics 10
1 4 Discrete methods 14
1 5 Finite differences and computational molecules 15
1 6 Finite difference operators 19
1 7 Errors 23
1 8 Stability and convergence 28
1 9 Irregular boundaries 30
1 10 Choice of discrete network 33
1 11 Dimensionless forms 34
References 39
2 Parabolic equations
2 0 Introduction 41
2 1 Simple explicit methods 42
2 2 Fourier stability method 47
2 3 Implicit methods 49
2 4 An unconditionally unstable difference equation 55
2 5 Matrix stability analysis 56
2 6 Extension of matrix stability analysis 59
2 7 Consistency, stability, and convergence 61
2 8 Pure initial value problems 62
2 9 Variable coefficients 64
2 10 Examples of equations with variable coefficients 68
2 11 General concepts of error reduction 70
2 12 Explicit methods for nonlinear problems 73
2 13 An application of the explicit method 77
2 14 Implicit methods for nonlinear problems 82
2 15 Concluding remarks 89
References 90
3 Elliptic equations
3 0 Introduction 92
3 1 Simple finite difference schemes 94
viii CONTENTS
3 2 Iterative methods 98
3 3 Linear elliptic equations 100
3 4 Some point iterative methods 103
3 5 Convergence of point iterative methods 107
3 6 Rates of convergence 114
3 7 Accelerations—successive over relaxation (SOR) 119
3 8 Extensions of SOR 125
3 9 Qualitative examples of over relaxation 130
3 10 Other point iterative methods 135
3 11 Block iterative methods 144
3 12 Alternating direction methods 148
3 13 Summary of ADI results 152
3 14 Some nonlinear examples I58
References 161
4 Hyperbolic equations
4 0 Introduction 165
4 1 The quasilinear system 170
4 2 Introductory examples 176
4 3 Method of characteristics 180
4 4 Constant states and simple waves 185
4 5 Typical application of characteristics 186
4 6 Explicit finite difference methods 193
4 7 Overstability 197
4 8 Implicit methods for second order equations 199
4 9 Nonlinear examples 201
4 10 Simultaneous first order equations—explicit methods 203
4 11 An implicit method for first order equations 209
4 12 Hybrid methods for first order equations 209
4 13 Gas dynamics in one space variable 212
4 14 Eulerian difference equations 214
4 15 Lagrangian difference equations 219
4 16 Hopscotch methods for conservation laws 221
4 17 Explicit implicit schemes for conservation laws 224
References 227
5 Special topics
5 0 Introduction 230
5 1 Singularities 230
5 2 Shocks 238
5 3 Eigenvalue problems 244
5 4 Parabolic equations in several space variables 251
5 5 Additional comments on elliptic equations 255
5 6 Hyperbolic equations in higher dimensions 262
5 7 Mixed systems 270
5 8 Higher order equations in elasticity and vibrations 274
5 9 Fluid mechanics: the Navier Stokes equations 281
5 10 Introduction to Monte Carlo methods 299
5 11 Method of lines 302
CONTENTS ix
5 12 Fast Fourier transform and applications 304
5 13 Method of fractional steps 307
References 311
6 Weighted residuals and finite elements
6 0 Introduction 320
6 1 Weighted residual methods (WRM) 320
6 2 Orthogonal collocation 325
6 3 Bubnov Galerkin (B G) method 329
6 4 Remarks on completeness, convergence, and errors bounds 333
6 5 Nagumo s lemma and application 339
6 6 Introduction to finite elements 342
References 348
Author index 351
Subject index 357
|
| any_adam_object | 1 |
| author | Ames, William F. |
| author_facet | Ames, William F. |
| author_role | aut |
| author_sort | Ames, William F. |
| author_variant | w f a wf wfa |
| building | Verbundindex |
| bvnumber | BV005699522 |
| callnumber-first | Q - Science |
| callnumber-label | QA374 |
| callnumber-raw | QA374 |
| callnumber-search | QA374 |
| callnumber-sort | QA 3374 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 920 |
| ctrlnum | (OCoLC)2894048 (DE-599)BVBBV005699522 |
| dewey-full | 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV005699522 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T11:42:24Z |
| institution | BVB |
| isbn | 0120567601 0177710861 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003560020 |
| oclc_num | 2894048 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XIV, 365 S. graph. Darst. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Academic Press [u.a.] |
| record_format | marc |
| series2 | Applications of mathematics series. Computer science and applied mathematics |
| spellingShingle | Ames, William F. Numerical methods for partial differential equations Equations aux dérivées partielles - Solutions numériques ram Équations aux dérivées partielles - Solutions numériques Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Lösung Chemie (DE-588)4036159-7 gnd Differentialgleichung (DE-588)4012249-9 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Numerische Mathematik (DE-588)4042805-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4131213-2 (DE-588)4036159-7 (DE-588)4012249-9 (DE-588)4173245-5 (DE-588)4014485-9 (DE-588)4042805-9 (DE-588)4128130-5 |
| title | Numerical methods for partial differential equations |
| title_auth | Numerical methods for partial differential equations |
| title_exact_search | Numerical methods for partial differential equations |
| title_full | Numerical methods for partial differential equations William F. Ames |
| title_fullStr | Numerical methods for partial differential equations William F. Ames |
| title_full_unstemmed | Numerical methods for partial differential equations William F. Ames |
| title_short | Numerical methods for partial differential equations |
| title_sort | numerical methods for partial differential equations |
| topic | Equations aux dérivées partielles - Solutions numériques ram Équations aux dérivées partielles - Solutions numériques Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Lösung Chemie (DE-588)4036159-7 gnd Differentialgleichung (DE-588)4012249-9 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Numerische Mathematik (DE-588)4042805-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Equations aux dérivées partielles - Solutions numériques Équations aux dérivées partielles - Solutions numériques Differential equations, Partial Numerical solutions Partielle Differentialgleichung Hyperbolische Differentialgleichung Lösung Chemie Differentialgleichung Parabolische Differentialgleichung Elliptische Differentialgleichung Numerische Mathematik Numerisches Verfahren |
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