Numerical analysis of partial differential equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2011
|
| Series: | Pure and applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Enth. Literaturverz. S. 477 - 482 und Index |
| Physical Description: | XIII, 487 S. graph. Darst. |
| ISBN: | 9780470647288 9781118111130 |
Staff View
MARC
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| 245 | 1 | 0 | |a Numerical analysis of partial differential equations |c S. H. Lui |
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| 300 | |a XIII, 487 S. |b graph. Darst. | ||
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| 500 | |a Enth. Literaturverz. S. 477 - 482 und Index | ||
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Record in the Search Index
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| adam_text |
CONTENTS
Table
(
jf Contents
Preface
Acknowledgments
1
Finite Difference
1.1
Second-Order Approximation for
Δ
1.2
Fourth-Order Approximation for
Δ
1.3
Neumann Boundary Condition
1.4
Polar Coordinates
1.5
Curved Boundary
1.6
Difference Approximation for
Δ2
1.7
A Convection-Diffusion Equation
1.8
Appendix: Analysis of Discrete Operators
.9
Summary and Exercises
V
ix
xiii
1
15
19
24
26
30
32
35
37
Mathematical Theory of Elliptic PDEs
45
2.1
Function Spaces
45
2.2
Derivatives
48
VÍ
CONTENTS
2.3
Sobolev
Spaces 52
2.4
Sobolev
Embedding Theory
56
2.5
Traces
59
2.6
Negative Sobolev Spaces
62
2.7
Some Inequalities and Identities
64
2.8
Weak Solutions
67
2.9
Linear Elliptic PDEs
74
2.10
Appendix: Some Definitions and Theorems
82
2.11
Summary and Exercises
88
Finite Elements
95
3.1
Approximate Methods of Solution
95
3.2
Finite Elements in ID
101
3.3
Finite Elements in 2D
109
3.4
Inverse Estimate
119
3.5
L2 and Negative-Norm Estimates
122
3.6
Higher-Order Elements
125
3.7
A Posteriori Estimate
133
3.8
Quadrilateral Elements
136
3.9
Numerical Integration
138
3.10
Stokes Problem
144
3.11
Linear Elasticity
156
3.12
Summary and Exercises
160
Numerical Linear Algebra
169
4.1
Condition Number
169
4.2
Classical Iterative Methods
173
4.3
Krylov Subspace Methods
178
4.4
Direct Methods
190
4.5
Preconditioning
196
4.6
Appendix: Chebyshev Polynomials
208
4.7
Summary and Exercises
210
Spectral Methods
221
5.1
Trigonometric Polynomials
221
5.2
Fourier Spectral Method
232
5.3
Orthogonal Polynomials
242
5.4
Spectral Galerkin and Spectral
Tau
Methods
262
CONTENTS
VII
5.5
Spectral Collocation
264
5.6
Polar Coordinates
278
5.7
Neumann Problems
280
5.8
Fourth-Order PDEs
281
5.9
Summary and Exercises
282
Evolutionary PDEs
291
6.1
Finite Difference Schemes for Heat Equation
292
6.2
Other Time Discretization Schemes
311
6.3
Convection-Dominated equations
315
6.4
Finite Element Scheme for Heat Equation
317
6.5
Spectral Collocation for Heat Equation
321
6.6
Finite Difference Scheme for Wave Equation
322
6.7
Dispersion
327
6.8
Summary and Exercises
332
Multigrid
345
7.1
Introduction
346
7.2
Two-Grid Method
349
7.3
Practical Multigrid Algorithms
351
7.4
Finite Element Multigrid
354
7.5
Summary and Exercises
363
Domain Decomposition
369
8.1
Overlapping
Schwarz
Methods
370
8.2
Orthogonal Projections
374
8.3
Non-overlapping
Schwarz
Method
382
8.4
Substructuring Methods
387
8.5
Optimal Substructuring Methods
395
8.6
Summary and Exercises
410
Infinite Domains
419
9.
1 Absorbing Boundary Conditions
420
9.2
Dirichlet-Neumann Map
424
9.3
Perfectly Matched Layer
427
9.4
Boundary Integral Methods
430
9.5
Fast Multipole Method
433
VIU
CONTENTS
9.6
Summary and Exercises
436
10
Nonlinear Problems
441
441
446
449
467
468
469
Answers to Selected Exercises
471
References
477
Index
483
10.1
Newton's Method
10.2
Other Methods
10.3
Some Nonlinear Problems
10.4
Software
10.5
Program Verification
10.6
Summary and Exercises
A balanced guide to the essential techniques for
solving elliptic partial differential equations
Numerical Analysis of Partial Differential Equations
provides a comprehensive, self-contained treatment of
the quantitative methods used to solve elliptic partial
differential equations (PDEs), with a focus on the efficiency
as well as the error of the presented methods. The author utilizes
coverage of theoretical PDEs, along with the numerical solution of linear
systems and various examples and exercises, to supply readers with an
introduction to the essential concepts in the numerical analysis of PDEs.
The book presents the three main discretization methods of elliptic
PDEs: finite difference, finite elements, and spectral methods. Each topic
has its own devoted chapters and is discussed alongside additional key
topics, including:
•
The mathematical theory of elliptic PDEs
•
Numerical linear algebra
•
Time-dependent PDEs
•
Multigrid and domain decomposition
•
PDEs posed on infinite domains
The book concludes with a discussion of the methods for nonlinear
problems, such as Newton's method, and addresses the importance of
hands-on work to facilitate learning. Each chapter concludes with a
set of exercises, including theoretical and programming problems, that
allows readers to test their understanding of the presented theories and
techniques. In addition, the book discusses important nonlinear problems
in many fields of science and engineering, providing information as to how
they can serve as computing projects across various disciplines.
Requiring only a preliminary understanding of analysis, Numerical Analysis
of Partial Differential Equations is suitable for courses on numerical PDEs at
the upper-undergraduate and graduate levels. The book is also appropriate
for students majoring in the mathematical sciences and engineering.
S. H. LUI, PhD,
is Associate Professor of Mathematics in the Department of
Mathematics at the University of Manitoba, Canada.
ISBN
Т70-0-Ч70-Ь47йв-а
90000
780470ll647288 |
| any_adam_object | 1 |
| author | Lui, Shaun H. 1961- |
| author_GND | (DE-588)101654636X |
| author_facet | Lui, Shaun H. 1961- |
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| author_sort | Lui, Shaun H. 1961- |
| author_variant | s h l sh shl |
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| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518/.64 |
| dewey-search | 518/.64 |
| dewey-sort | 3518 264 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV039700484 |
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| indexdate | 2025-03-31T20:04:53Z |
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| isbn | 9780470647288 9781118111130 |
| language | English |
| lccn | 2011013570 |
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| publisher | Wiley |
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| series2 | Pure and applied mathematics |
| spelling | Lui, Shaun H. 1961- Verfasser (DE-588)101654636X aut Numerical analysis of partial differential equations S. H. Lui Hoboken, NJ Wiley 2011 XIII, 487 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Enth. Literaturverz. S. 477 - 482 und Index Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Erscheint auch als Online-Ausgabe, EPUB 978-1-118-11111-6 Erscheint auch als Online-Ausgabe, PDF 978-1-118-11110-9 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024549049&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024549049&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Lui, Shaun H. 1961- Numerical analysis of partial differential equations Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4128130-5 |
| title | Numerical analysis of partial differential equations |
| title_auth | Numerical analysis of partial differential equations |
| title_exact_search | Numerical analysis of partial differential equations |
| title_full | Numerical analysis of partial differential equations S. H. Lui |
| title_fullStr | Numerical analysis of partial differential equations S. H. Lui |
| title_full_unstemmed | Numerical analysis of partial differential equations S. H. Lui |
| title_short | Numerical analysis of partial differential equations |
| title_sort | numerical analysis of partial differential equations |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Partielle Differentialgleichung Numerisches Verfahren |
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