A first course in integral equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1997
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 205 - 206 |
| Beschreibung: | XI, 208 S |
| ISBN: | 9810231016 |
Internformat
MARC
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| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1997 | |
| 300 | |a XI, 208 S | ||
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| 500 | |a Literaturverz. S. 205 - 206 | ||
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Datensatz im Suchindex
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Contents
1 Introductory Concepts 1
1.1 Definitions . 1
1.2 Classification of Linear Integral Equations 3
1.2.1 Fredholm Linear Integral Equations: 3
1.2.2 Volterra Linear Integral Equations: 4
1.2.3 Integro-Differential Equations: 6
1.2.4 Singular Integral Equations: 7
1.3 Solution of an Integral Equation 11
1.4 Converting Volterra Equation to ODE 15
1.5 Converting IVP to Volterra Equation 20
1.6 Converting BVP to Fredholm Equation 26
2 Fredholm Integral Equations 31
2.1 Introduction 31
2.2 The Decomposition Method 33
2.2.1 The Modified Decomposition Method: 38
2.3 The Direct Computation Method 43
2.4 The Successive Approximations Method 48
2.5 The Method of Successive Substitutions 52
2.6 Comparison between Alternative Methods 56
2.7 Homogeneous Fredholm Equations 59
3 Volterra Integral Equations 67
3.1 Introduction 67
3.2 The Adomian Decomposition Method 68
3.2.1 The Modified Decomposition Method: 73
3.3 The Series Solution Method 77
v
vi CONTENTS
3.4 Converting Volterra Equation to IVP 82
3.5 Successive Approximations Method 86
3.6 The Method of Successive Substitutions 91
3.7 Comparison between Alternative Methods 95
3.8 Volterra Equations of the First Kind 99
4 Integro-DiflGerential Equations 103
41 Introduction 103
42 Fredholm Integra-Differential Equations 105
42.1 The Direct Computation Method: 105
42.2 The Adomian Decomposition Method: 109
42.3 Converting to Fredholm Integral Equations: . 118
43 Volterra Integro-Differential Equations 121
43.1 The Series Solution Method: 121
43.2 The Decomposition Method: 126
43.3 Converting to Volterra Integral Equation: . 131
43.4 Converting to Initial Value Problems: 134
5 Singular Integral Equations 139
5.1 Definitions 139
5.2 Abel's Problem 141
5.2.1 The Generalized Abel's Integral Equation . 146
5.3 The Weakly-Singular Volterra Equations 150
6 Nonlinear Integral Equations 157
6.1 Definitions 157
6.2 Nonlinear Fredholm Integral Equations 158
6.2.1 The Direct Computation Method 159
6.2.2 The Decomposition Method 163
6.3 Nonlinear Volterra Integral Equations 173
6.3.1 The Series Solution Method 173
6.3.2 The Decomposition Method 177
A Table of Integrals 183
B Integrals of Irrational Functions 187
C Series Representations 189 '
CONTENTS vii
D The Error and Gamma Functions 191
Answers To Exercises 193
Bibliography 205
Index 207 |
| adam_txt |
Contents
1 Introductory Concepts 1
1.1 Definitions . 1
1.2 Classification of Linear Integral Equations 3
1.2.1 Fredholm Linear Integral Equations: 3
1.2.2 Volterra Linear Integral Equations: 4
1.2.3 Integro-Differential Equations: 6
1.2.4 Singular Integral Equations: 7
1.3 Solution of an Integral Equation 11
1.4 Converting Volterra Equation to ODE 15
1.5 Converting IVP to Volterra Equation 20
1.6 Converting BVP to Fredholm Equation 26
2 Fredholm Integral Equations 31
2.1 Introduction 31
2.2 The Decomposition Method 33
2.2.1 The Modified Decomposition Method: 38
2.3 The Direct Computation Method 43
2.4 The Successive Approximations Method 48
2.5 The Method of Successive Substitutions 52
2.6 Comparison between Alternative Methods 56
2.7 Homogeneous Fredholm Equations 59
3 Volterra Integral Equations 67
3.1 Introduction 67
3.2 The Adomian Decomposition Method 68
3.2.1 The Modified Decomposition Method: 73
3.3 The Series Solution Method 77
v
vi CONTENTS
3.4 Converting Volterra Equation to IVP 82
3.5 Successive Approximations Method 86
3.6 The Method of Successive Substitutions 91
3.7 Comparison between Alternative Methods 95
3.8 Volterra Equations of the First Kind 99
4 Integro-DiflGerential Equations 103
41 Introduction 103
42 Fredholm Integra-Differential Equations 105
42.1 The Direct Computation Method: 105
42.2 The Adomian Decomposition Method: 109
42.3 Converting to Fredholm Integral Equations: . 118
43 Volterra Integro-Differential Equations 121
43.1 The Series Solution Method: 121
43.2 The Decomposition Method: 126
43.3 Converting to Volterra Integral Equation: . 131
43.4 Converting to Initial Value Problems: 134
5 Singular Integral Equations 139
5.1 Definitions 139
5.2 Abel's Problem 141
5.2.1 The Generalized Abel's Integral Equation . 146
5.3 The Weakly-Singular Volterra Equations 150
6 Nonlinear Integral Equations 157
6.1 Definitions 157
6.2 Nonlinear Fredholm Integral Equations 158
6.2.1 The Direct Computation Method 159
6.2.2 The Decomposition Method 163
6.3 Nonlinear Volterra Integral Equations 173
6.3.1 The Series Solution Method 173
6.3.2 The Decomposition Method 177
A Table of Integrals 183
B Integrals of Irrational Functions 187
C Series Representations 189 '
CONTENTS vii
D The Error and Gamma Functions 191
Answers To Exercises 193
Bibliography 205
Index 207 |
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| index_date | 2024-07-02T22:31:33Z |
| indexdate | 2024-08-15T00:17:24Z |
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| isbn | 9810231016 |
| language | English |
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| spelling | Wazwaz, Abdul-Majid Verfasser aut A first course in integral equations Abdul-Hajid Wazwaz Singapore [u.a.] World Scientific 1997 XI, 208 S txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 205 - 206 Integral equations Integralgleichung (DE-588)4027229-1 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Integralgleichung (DE-588)4027229-1 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016835046&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 | Wazwaz, Abdul-Majid A first course in integral equations Integral equations Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4027229-1 (DE-588)4123623-3 |
| title | A first course in integral equations |
| title_auth | A first course in integral equations |
| title_exact_search | A first course in integral equations |
| title_exact_search_txtP | A first course in integral equations |
| title_full | A first course in integral equations Abdul-Hajid Wazwaz |
| title_fullStr | A first course in integral equations Abdul-Hajid Wazwaz |
| title_full_unstemmed | A first course in integral equations Abdul-Hajid Wazwaz |
| title_short | A first course in integral equations |
| title_sort | a first course in integral equations |
| topic | Integral equations Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Integral equations Integralgleichung Lehrbuch |
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