Analytical and numerical methods for Volterra equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
Siam
1985
|
| Series: | Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 227 S. |
| ISBN: | 0898711983 |
Staff View
MARC
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| 100 | 1 | |a Linz, Peter |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analytical and numerical methods for Volterra equations |
| 264 | 1 | |a Philadelphia |b Siam |c 1985 | |
| 300 | |a XIII, 227 S. | ||
| 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 7 | |
| 650 | 7 | |a Equacoes integrais (engenharia eletrica) |2 larpcal | |
| 650 | 7 | |a Numerieke methoden |2 gtt | |
| 650 | 7 | |a Volterra, Équations de - Solutions numériques |2 ram | |
| 650 | 7 | |a Volterra-integraalvergelijkingen |2 gtt | |
| 650 | 7 | |a équation intégrale |2 inriac | |
| 650 | 4 | |a Volterra equations |x Numerical solutions | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xi
Part A: Theory
Chapter 1. Introduction 3
1.1. Classification of Volterra equations 3
1.2. Connection between Volterra equations and initial value prob¬
lems 7
Notes on Chapter 1 10
Chapter 2. Some Applications of Volterra Equations 13
2.1. History dependent problems 14
2.2. Applications in systems theory 15
2.3. Problems in heat conduction and diffusion 19
2.4. Some problems in experimental inference 23
Notes on Chapter 2 26
Chapter 3. Linear Volterra Equations of the Second Kind 29
3.1. Existence and uniqueness of the solution 29
3.2. The resolvent kernel 35
3.3. Some qualitative properties of the solution 38
3.4. Systems of equations 46
3.5. Equations with unbounded kernels 47
3.6. Integrodifferential equations 49
Notes on Chapter 3 50
Chapter 4. Nonlinear Equations of the Second Kind 51
4.1. Successive approximations for Lipschitz continuous kernels . 51
4.2. Existence and uniqueness for more general kernels 54
vii
Viii CONTENTS
4.3. Properties of the solution 58
4.4. Unbounded kernels and systems of equations 62
4.5. The resolvent equation 63
Notes on Chapter 4 65
Chapter 5. Equations of the First Kind 67
5.1. Equations with smooth kernels 67
5.2. Abel equations 71
Notes on Chapter 5 76
Chapter 6. Convolution Equations 77
6.1. Some simple kernels 77
6.2. Laplace transforms 84
6.3. Solution methods using Laplace transforms 86
6.4. The asymptotic behavior of the solution for some special
equations 89
Notes on Chapter 6 92
Part B: Numerical Methods
Chapter 7. The Numerical Solution of Equations of the Second Kind . 95
7.1. A simple numerical procedure 96
7.2. Methods based on more accurate numerical integration ... 97
7.3. Error analysis: convergence of the approximate solution ... 100
7.4. Error estimates and numerical stability 103
7.5. Another view of stability 110
7.6. Block by block methods 114
7.7. Some numerical examples 118
7.8. Explicit Runge Kutta methods 122
7.9. A summary of related ideas and methods 124
Notes on Chapter 7 127
Chapter 8. Product Integration Methods for Equations of the Second
Kind 129
8.1. Product integration 130
8.2. A simple method for a specific example 132
8.3. A method based on the product trapezoidal rule 135
8.4. A block by block method based on quadratic interpolation . 136
8.5. A convergence proof for product integration methods .... 138
Notes on Chapter 8 141
CONTENTS ix
Chapter 9. Equations of the First Kind with Differentiable Kernels 143
9.1. Application of simple integration rules 144
9.2. Error analysis for simple approximation methods 145
9.3. Difficulties with higher order methods 151
9.4. Block by block methods 154
9.5. Use of the differentiated form 158
9.6. Nonlinear equations 160
9.7. Some practical considerations 161
Notes on Chapter 9 163
Chapter 10. Equations of the Abel Type 165
10.1. Solving a simple Abel equation 166
10.2. The midpoint and trapezoidal methods for general Abel
equations 166
10.3. Block by block methods 169
10.4. Some remarks on error analysis 171
10.5. Solving Abel equations in the presence of experimental errors 174
Notes on Chapter 10 175
Chapter 11. Integrodifferential Equations 177
11.1. A simple numerical method 178
11.2. Linear multistep methods 182
11.3. Block by block methods 185
11.4. Numerical stability 186
11.5. Other types of integrodifferential and functional equations . 188
Notes on Chapter 11 189
Chapter 12. Some Computer Programs 191
12.1. The trapezoidal method for systems of the second kind . . 192
12.2. The product trapezoidal method for a system of the second
kind 195
12.3. The midpoint method for systems of the first kind 197
12.4. The product midpoint method for a system of the first kind. 198
Notes on Chapter 12 199
Chapter 13. Case Studies 201
13.1. Estimating errors in the approximation 201
13.2. An example from polymer rheology 204
X CONTENTS
13.3. Solving an equation of the first kind in the presence of large
data errors 207
Notes on Chapter 13 211
References 213
Supplementary Bibliography 223
Index 225
|
| any_adam_object | 1 |
| author | Linz, Peter |
| author_facet | Linz, Peter |
| author_role | aut |
| author_sort | Linz, Peter |
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| bvnumber | BV009218754 |
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| ctrlnum | (OCoLC)12336187 (DE-599)BVBBV009218754 |
| dewey-full | 515.4/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.4/5 |
| dewey-search | 515.4/5 |
| dewey-sort | 3515.4 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T17:33:19Z |
| institution | BVB |
| isbn | 0898711983 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006128647 |
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| physical | XIII, 227 S. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| 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 | Linz, Peter Verfasser aut Analytical and numerical methods for Volterra equations Philadelphia Siam 1985 XIII, 227 S. txt rdacontent n rdamedia nc rdacarrier Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics 7 Equacoes integrais (engenharia eletrica) larpcal Numerieke methoden gtt Volterra, Équations de - Solutions numériques ram Volterra-integraalvergelijkingen gtt équation intégrale inriac Volterra equations Numerical solutions Volterra-Integralgleichung (DE-588)4234593-5 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Volterra-Gleichungen (DE-588)4137459-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Volterra-Integralgleichung (DE-588)4234593-5 s Numerisches Verfahren (DE-588)4128130-5 s Integralgleichung (DE-588)4027229-1 s 1\p DE-604 Volterra-Gleichungen (DE-588)4137459-9 s 2\p DE-604 Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics 7 (DE-604)BV001889480 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006128647&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Linz, Peter Analytical and numerical methods for Volterra equations Society for Industrial and Applied Mathematics: SIAM studies in applied mathematics Equacoes integrais (engenharia eletrica) larpcal Numerieke methoden gtt Volterra, Équations de - Solutions numériques ram Volterra-integraalvergelijkingen gtt équation intégrale inriac Volterra equations Numerical solutions Volterra-Integralgleichung (DE-588)4234593-5 gnd Integralgleichung (DE-588)4027229-1 gnd Volterra-Gleichungen (DE-588)4137459-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4234593-5 (DE-588)4027229-1 (DE-588)4137459-9 (DE-588)4128130-5 |
| title | Analytical and numerical methods for Volterra equations |
| title_auth | Analytical and numerical methods for Volterra equations |
| title_exact_search | Analytical and numerical methods for Volterra equations |
| title_full | Analytical and numerical methods for Volterra equations |
| title_fullStr | Analytical and numerical methods for Volterra equations |
| title_full_unstemmed | Analytical and numerical methods for Volterra equations |
| title_short | Analytical and numerical methods for Volterra equations |
| title_sort | analytical and numerical methods for volterra equations |
| topic | Equacoes integrais (engenharia eletrica) larpcal Numerieke methoden gtt Volterra, Équations de - Solutions numériques ram Volterra-integraalvergelijkingen gtt équation intégrale inriac Volterra equations Numerical solutions Volterra-Integralgleichung (DE-588)4234593-5 gnd Integralgleichung (DE-588)4027229-1 gnd Volterra-Gleichungen (DE-588)4137459-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Equacoes integrais (engenharia eletrica) Numerieke methoden Volterra, Équations de - Solutions numériques Volterra-integraalvergelijkingen équation intégrale Volterra equations Numerical solutions Volterra-Integralgleichung Integralgleichung Volterra-Gleichungen Numerisches Verfahren |
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