Fourier analysis of numerical approximations of hyperbolic equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
siam
1982
|
| Schriftenreihe: | Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics.
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 140 Seiten Diagramme |
| ISBN: | 0898711819 0898713927 |
Internformat
MARC
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| 100 | 1 | |a Vichnevetsky, Robert |0 (DE-588)133301583 |4 aut | |
| 245 | 1 | 0 | |a Fourier analysis of numerical approximations of hyperbolic equations |c Robert Vichnevetsky and John B. Bowles |
| 264 | 1 | |a Philadelphia |b siam |c 1982 | |
| 300 | |a XII, 140 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics. |v 5 | |
| 650 | 7 | |a Analise Numerica |2 larpcal | |
| 650 | 4 | |a Analyse numérique | |
| 650 | 4 | |a Fourier, Analyse de | |
| 650 | 7 | |a Fourier, Analyse de |2 ram | |
| 650 | 7 | |a analyse Fourier |2 inriac | |
| 650 | 7 | |a approximation numérique |2 inriac | |
| 650 | 7 | |a transformation Fourier |2 inriac | |
| 650 | 4 | |a Équations différentielles hyperboliques - Solutions numériques | |
| 650 | 7 | |a équation hyperbolique |2 inriac | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Differential equations, Hyperbolic |x Numerical solutions | |
| 650 | 4 | |a Fourier analysis | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hyperbolische Differentialgleichung |0 (DE-588)4131213-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hyperbolische Differentialgleichung |0 (DE-588)4131213-2 |D s |
| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | 2 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Bowles, John B. |0 (DE-588)1242345825 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 9781611970876 |
| 830 | 0 | |a Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics. |v 5 |w (DE-604)BV001889480 |9 5 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-001320129 | ||
Datensatz im Suchindex
| _version_ | 1804116470266855424 |
|---|---|
| adam_text | Contents
Foreword ix
Preface xi
Chapter 1. Introduction 1
1.1 Introduction 1
1.2 Linear models of hyperbolic equations 2
1.3 Approximation 4
1.4 Finite element Galerkin semi discretizations 5
1.5 Toeplitz operators 7
1.6 B spline Galerkin semi discretizations 8
1.7 Fully discrete approximations 11
1.8 Fourier analysis 12
1.9 i?2 norms and Parseval s equality 12
1.10 Relationship between continuous and discrete transforms . 13
1.11 Fourier analysis of numerical approximations 16
1.12 Sampling of the initial data 16
Chapter 2. Fourier Analysis of the Accuracy of Semi Discretizations 19
2.1 Introduction 19
2.2 Sinusoidal trial solutions 19
2.3 Fourier transforms and global errors 23
2.4 Relation to classical truncation error analysis 24
2.5 Finite element Galerkin semi discretizations 26
2.6 A generalization 27
2.7 Semi discretization of a conservation law 29
2.8 Time frequency 30
2.9 The wave equation 31
2.10 Implicit semi discretizations of the wave equation .... 33
Chapter 3. Higher Order Semi Discretizations 35
3.1 Synthesis in the frequency domain 35
3.2 Velocity error 37
3.3 Limiting case (K oo) 37
3.4 Relation to the cardinal function 37
V
vi CONTENTS
3.5 B spline Galerkin semi discretizations 40
3.6 An equivalence of bases 40
3.7 Equivalence with collocation 41
3.8 Fourier analysis of the algorithms obtained with B splines . 43
3.9 Convergence rates 43
3.10 B spline semi discretizations of the wave equation ... 46
3.11 Analysis 48
Chapter 4. Full Discretizations 51
4.1 Fourier analysis 51
4.2 Stability 54
4.3 Velocity and amplitude error 58
4.4 Examples 59
4.5 Time marching methods for second order equations ... 61
Chapter 5. Damping, Diffusion and Filtering 63
5.1 Spurious diffusion 63
5.2 Limitations of the spurious diffusion model 65
5.3 Spurious diffusion in discretizations of the wave equation . 66
5.4 Filtering 69
5.5 Low pass niters 70
5.6 Flat low pass filters 70
5.7 Fast Fourier transform filtering 71
5.8 Effect of filtering on damping and numerical stability ... 74
Chapter 6. Group Velocity 75
6.1 Introduction 75
6.2 Group velocity and energy propagation 77
6.3 Group velocity of the simple 3 point finite differences semi
discretization 77
6.4 Group velocity of other 3 point semi discretizations ... 78
6.5 Wave analysis 80
6.6 Wave analysis of other semi discretizations 82
Chapter 7. Time Fourier Transforms 85
7.1 Introduction 85
7.2 Numerical phase velocity and wavelength 87
7.3 Relation to ^ Fourier transforms 90
7.4 Cut off frequency 92
7.5 Energy 95
7.6 Group velocity of the two fundamental types of solutions . 95
CONTENTS vii
7.7 Reflection at a downstream boundary 97
7.8 Convergence rates 99
7.9 A 3 point boundary formula 101
Chapter 8. Fourier Analysis and i?2 Norm of the Global Error . 103
8.1 Introduction 103
8.2 Examples 104
8.3 Relation with convergence rates analysis 107
8.4 Asymptotic approximations 107
Chapter 9. Spectral Methods 109
9.1 Introduction 109
9.2 Truncated Fourier series method 110
9.3 Analysis Ill
9.4 Fourier collocation method 112
Chapter 10. Equations in Two Dimensions: Anisotropy 115
10.1 The advection equation in two dimensions 115
10.2 Anisotropy of the approximation on a square grid .... 116
10.3 Analysis of other explicit formulae 119
10.4 Implicit approximations 120
10.5 The wave equation in the plane 122
10.6 9 point semi discretizations of the wave equation .... 128
Bibliography 131
Index 137
|
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| author | Vichnevetsky, Robert Bowles, John B. |
| author_GND | (DE-588)133301583 (DE-588)1242345825 |
| author_facet | Vichnevetsky, Robert Bowles, John B. |
| author_role | aut aut |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/53 |
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| dewey-sort | 3515.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002020938 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:39:01Z |
| institution | BVB |
| isbn | 0898711819 0898713927 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001320129 |
| oclc_num | 9185877 |
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| owner_facet | DE-91G DE-BY-TUM DE-384 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| physical | XII, 140 Seiten Diagramme |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | siam |
| record_format | marc |
| series | Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics. |
| series2 | Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics. |
| spelling | Vichnevetsky, Robert (DE-588)133301583 aut Fourier analysis of numerical approximations of hyperbolic equations Robert Vichnevetsky and John B. Bowles Philadelphia siam 1982 XII, 140 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics. 5 Analise Numerica larpcal Analyse numérique Fourier, Analyse de Fourier, Analyse de ram analyse Fourier inriac approximation numérique inriac transformation Fourier inriac Équations différentielles hyperboliques - Solutions numériques équation hyperbolique inriac Approximation theory Differential equations, Hyperbolic Numerical solutions Fourier analysis Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 s Numerisches Verfahren (DE-588)4128130-5 s Harmonische Analyse (DE-588)4023453-8 s DE-604 Bowles, John B. (DE-588)1242345825 aut Erscheint auch als Online-Ausgabe 9781611970876 Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics. 5 (DE-604)BV001889480 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001320129&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vichnevetsky, Robert Bowles, John B. Fourier analysis of numerical approximations of hyperbolic equations Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics. Analise Numerica larpcal Analyse numérique Fourier, Analyse de Fourier, Analyse de ram analyse Fourier inriac approximation numérique inriac transformation Fourier inriac Équations différentielles hyperboliques - Solutions numériques équation hyperbolique inriac Approximation theory Differential equations, Hyperbolic Numerical solutions Fourier analysis Numerisches Verfahren (DE-588)4128130-5 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4131213-2 (DE-588)4023453-8 |
| title | Fourier analysis of numerical approximations of hyperbolic equations |
| title_auth | Fourier analysis of numerical approximations of hyperbolic equations |
| title_exact_search | Fourier analysis of numerical approximations of hyperbolic equations |
| title_full | Fourier analysis of numerical approximations of hyperbolic equations Robert Vichnevetsky and John B. Bowles |
| title_fullStr | Fourier analysis of numerical approximations of hyperbolic equations Robert Vichnevetsky and John B. Bowles |
| title_full_unstemmed | Fourier analysis of numerical approximations of hyperbolic equations Robert Vichnevetsky and John B. Bowles |
| title_short | Fourier analysis of numerical approximations of hyperbolic equations |
| title_sort | fourier analysis of numerical approximations of hyperbolic equations |
| topic | Analise Numerica larpcal Analyse numérique Fourier, Analyse de Fourier, Analyse de ram analyse Fourier inriac approximation numérique inriac transformation Fourier inriac Équations différentielles hyperboliques - Solutions numériques équation hyperbolique inriac Approximation theory Differential equations, Hyperbolic Numerical solutions Fourier analysis Numerisches Verfahren (DE-588)4128130-5 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Analise Numerica Analyse numérique Fourier, Analyse de analyse Fourier approximation numérique transformation Fourier Équations différentielles hyperboliques - Solutions numériques équation hyperbolique Approximation theory Differential equations, Hyperbolic Numerical solutions Fourier analysis Numerisches Verfahren Hyperbolische Differentialgleichung Harmonische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001320129&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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