An introduction to numerical methods for differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Marshfield, Massachusetts
Pitman publishing inc.
1981
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | ix, 329 Seiten |
| ISBN: | 0273016865 0273016377 |
Internformat
MARC
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| 245 | 1 | 0 | |a An introduction to numerical methods for differential equations |c James M. Ortega, Department of applied mathematics and computer science, University of Virginia ; William G. Poole, Jr., Boeing somputer services company |
| 264 | 1 | |a Marshfield, Massachusetts |b Pitman publishing inc. |c 1981 | |
| 300 | |a ix, 329 Seiten | ||
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| 650 | 4 | |a Datenverarbeitung | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface v
CHAPTER 1 The World of Scientific Computing 1
1.1 What Is Scientific Computing 1
1.2 Mathematical Modeling 3
1.3 The Process of Numerical Solution 6
1.4 The Impact of Computer Science on Scientific
Computing 11
CHAPTER 2 Initial Value Problems in Ordinary Differential
Equations 22
2.1 Examples of Initial Value Problems 22
2.2 Numerical Solutions: One step Methods 28
2.3 Polynomial Interpolation 43
2.4 Numerical Solutions: Multistep Methods 50
2.5 Stability, Instability, and Stiff Equations 59
CHAPTER 3 Pinning It Down on Both Ends: Two Point
Boundary Value Problems 69
3.1 A Diffusion Problem 69
3.2 The Finite Difference Method for Linear Problems 74
iii
Contents
3.3 Solution of Systems of Linear Equations 84
3.4 Interchanges 96
3.5 Ill Conditioning and Error Analysis 105
CHAPTER 4 Life Is Really Nonlinear 119
4.1 Solution by the Shooting Method 119
4.2 Solution of Nonlinear Equations in a Single
Variable 124
4.3 Solution of Systems of Nonlinear Equations 137
4.4 Finite Difference Methods for Nonlinear Boundary Value
Problems 145
CHAPTER 5 Is There More to Computing Than Finite
Differences? 152
5.1 Introduction to Projection Methods 152
5.2 Spline and Least Squares Approximation 160
5.3 Numerical Integration 176
5.4 The Discrete Problem Using Splines 184
CHAPTER 6 n Important Numbers: Eigenvalue Computations 196
6.1 Examples of Eigenvalue Problems and Mathematical
Background 196
6.2 The Symmetric Eigenvalue Problem 209
6.3 The QR Method 220
6.4 Methods for Large Sparse Matrices 230
CHAPTER 7 Space and Time 236
7.1 Partial Differential Equations 236
7.2 Explicit Methods and the Stability Problem 243
7.3 Implicit Methods 252
7.4 Semidiscrete Methods 257
CHAPTER 8 The Curse of Dimensionality 263
8.1 Problems in Two and Three Space Dimensions 263
8.2 Discretization Problems in Two Space Dimensions 268
iv
Contents
8.3 Direct Methods for Large Sparse Systems 276
8.4 Interative Methods 288
Appendix 1 Basic Results from Analysis 305
Appendix 2 Ordinary Differential Equations 308
Appendix 3 Linear Algebra and Matrix Theory 311
Bibliography 317
Author Index 323
Subject Index 325
v
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:41:16Z |
| institution | BVB |
| isbn | 0273016865 0273016377 |
| language | English |
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| publishDate | 1981 |
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| spelling | Ortega, James M. 1932- (DE-588)114190852 aut An introduction to numerical methods for differential equations James M. Ortega, Department of applied mathematics and computer science, University of Virginia ; William G. Poole, Jr., Boeing somputer services company Marshfield, Massachusetts Pitman publishing inc. 1981 ix, 329 Seiten txt rdacontent n rdamedia nc rdacarrier Datenverarbeitung Mathematik Automatic Data Processing Differential equations Numerical solutions Data processing Mathematics Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Poole, William G. (DE-588)1063977797 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001415614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ortega, James M. 1932- Poole, William G. An introduction to numerical methods for differential equations Datenverarbeitung Mathematik Automatic Data Processing Differential equations Numerical solutions Data processing Mathematics Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4012249-9 |
| title | An introduction to numerical methods for differential equations |
| title_auth | An introduction to numerical methods for differential equations |
| title_exact_search | An introduction to numerical methods for differential equations |
| title_full | An introduction to numerical methods for differential equations James M. Ortega, Department of applied mathematics and computer science, University of Virginia ; William G. Poole, Jr., Boeing somputer services company |
| title_fullStr | An introduction to numerical methods for differential equations James M. Ortega, Department of applied mathematics and computer science, University of Virginia ; William G. Poole, Jr., Boeing somputer services company |
| title_full_unstemmed | An introduction to numerical methods for differential equations James M. Ortega, Department of applied mathematics and computer science, University of Virginia ; William G. Poole, Jr., Boeing somputer services company |
| title_short | An introduction to numerical methods for differential equations |
| title_sort | an introduction to numerical methods for differential equations |
| topic | Datenverarbeitung Mathematik Automatic Data Processing Differential equations Numerical solutions Data processing Mathematics Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Datenverarbeitung Mathematik Automatic Data Processing Differential equations Numerical solutions Data processing Mathematics Numerisches Verfahren Differentialgleichung |
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