Asymptotic methods for ordinary differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
2000
|
| Series: | Mathematics and its applications
512 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | X, 364 S. |
| ISBN: | 0792364007 |
Staff View
MARC
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| 245 | 1 | 0 | |a Asymptotic methods for ordinary differential equations |c by R. P. Kuzmina |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
PREFACE ix
Part 1. The Quasiregular Cauchy Problem 1
CHAPTER 1. SOLUTION EXPANSIONS OF THE
QUASIREGULAR CAUCHY PROBLEM 3
§ 1 Solution of the Quasiregular Cauchy Problem 3
§2 Statement of Theorems about the Quasiregular Cauchy
Problem 7
§3 Proof of Theorems 2.1 2.4 14
§4 Proof of Theorem s 2.5 2.8 23
§5 Proof of Theorem 2.9 . 36
§6 Proof of Theorem 2.10 40
§7 Proof of Theorem 2.11 . 42
§8 Examples of the Quasiregular Cauchy Problem 43
§9 The Regularly Perturbed Cauchy Problem 49
§10 Examples of, . the Regularly Perturbed Cauchy Problem ... 56
§11 Estimates of the Convergence Radius 65
§ 12 Estimates of the Convergence Time Interval 72
§13 Estimates of the Cauchy Matrix Norm, I 76
§14 Conclusions of Chapter 1 81
CHAPTER 2. THE VAN DER POL PROBLEM 83
§15 Reduction to the Quasiregular Cauchy Problem 83
§ 16 Solution Construction 88
§ 17 Application of Theorems on the Quasiregular Cauchy
Problem 93
§18 Numerical Estimates of the Asymptotic Solution Accuracy . 107
§19 More on the van der Pol Problem 119
§20 Conclusions of Chapter 2 127
§21 Conclusions of Part 1 127
vi TABLE OP CONTENTS
Part 2. The Tikhonov Problem 129
CHAPTER 3. THE BOUNDARY FUNCTIONS METHOD 131
§22 Definition of the Tikhonov Problem 131
§23 Construction of the Asymptotic Solution by the Boundary
Functions Method 132
§24 Algorithm for Computing the Asymptotics Coefficients . . 136
§25 Algorithm for Computing the Asymptotics Coefficients
for to = 2 141
§26 Conditions Imposed on the Singular Equations 144
§27 Conditions Imposed on the Singular Equations for m = 2 . 147
§28 Statements of Theorems about the Boundary Functions
Method 148
§29 Proof of Theorem 28.5 154
§30 Limiting Theorems 159
§31 Examples of Using the Boundary Functions Method .... 164
§32 Conclusions of Chapter 3 179
CHAPTER 4. PROOF OF THEOREMS 28.1 28.4 181
§33 The Functions yf] 181
§34 The Functions yf] 186
§35 The Functions y[k) 194
§36 Introduction of the Auxiliary Variable 198
§37 The Matrices V% 199
§38 The Functions Gt 203
§39 The Functions a, b, c 215
§40 Application of Theorem 28.5 229
§41 Conclusions of Chapter 4 230
CHAPTER 5. THE METHOD OF TWO PARAMETERS 231
§42 Construction of the Asymptotic Solution by the Method of
Two Parameters 231
§43 Statement of Theorems about the Method of Two
Parameters 232
§44 Proof of Theorems 43.1 43.4 236
§45 Proof of Theorems 43.5 43.8 249
§46 Proof of Theorem 43.9 262
§47 Examples of Using the Method of Two Parameters 268
§48 Conclusions of Chapter 5 271
TABLE OF CONTENTS vii
CHAPTER 6. THE MOTION OF A GYROSCOPE
MOUNTED IN GIMBALS 272
§49 Reduction to the Singularly Perturbed Problem 272
§50 Application of the Method of Boundary Functions 276
§51 Modification of the Method of Boundary Functions 286
§52 Application of the Method of Two Parameters 295
§53 Modification of the Method of Two Parameters 297
§54 Application of the Second Method of Lyapunov 298
§55 Connection of the Method of Boundary Functions and the
Method of Two Parameters with the Second Method of
Lyapunov 300
§56 The Motion of a Gyroscope Mounted in Gimbals and the
Regularly Perturbed Cauchy Problem 304
§57 Conclusions of Chapter 6 305
CHAPTER 7. SUPPLEMENT 306
§ 58 The Tikhonov Problem and the Regularly Perturbed Cauchy
Problem 306
§59 Proof of Theorems 58.1, 58.2 311
§60 Estimates of the Cauchy Matrix Norm, II 322
§61 Conclusions of Chapter 7 322
§62 Conclusions of Part 2 323
Part 3. The Double Singular Cauchy Problem 325
CHAPTER 8. THE BOUNDARY FUNCTIONS METHOD 327
§63 Definition of the Double Singular Cauchy Problem 327
§64 Construction of the Asymptotic Solution by the Boundary
Functions Method 328
§65 Algorithm for Computing the Coefficients of Asymptotics . 331
§66 Conditions Imposed on the Double Singular Cauchy
Problem 334
§67 Statement of Theorems about the Boundary Functions
Method 336
§68 Proof of Theorems 67.1 67.4 338
§69 Limiting Theorems 345
§70 Example of Using the Boundary Functions Method 346
§71 Conclusions of Chapter 8 349
viii TABLE OF CONTENTS
CHAPTER 9. THE METHOD OF TWO PARAMETERS 350
§ 72 Construction of the Asymptotic Solution by the Method of
Two Parameters 350
§73 Theorems on the Method of Two Parameters 351
§ 74 Example of Using the Method of Two Parameters 356
§75 Conclusions of Chapter 9 357
§76 Conclusions of Part 3 358
BIBLIOGRAPHY 359
INDEX 363
|
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| indexdate | 2024-07-09T18:53:20Z |
| institution | BVB |
| isbn | 0792364007 |
| language | English |
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| physical | X, 364 S. |
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| publisher | Kluwer |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Kuzmina, R. P. Verfasser aut Asymptotic methods for ordinary differential equations by R. P. Kuzmina Dordrecht [u.a.] Kluwer 2000 X, 364 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 512 Aus dem Russ. übers. Differential equations Asymptotic theory Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Asymptotische Methode (DE-588)4287476-2 s DE-604 Mathematics and its applications 512 (DE-604)BV008163334 512 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009481179&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kuzmina, R. P. Asymptotic methods for ordinary differential equations Mathematics and its applications Differential equations Asymptotic theory Asymptotische Methode (DE-588)4287476-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4287476-2 (DE-588)4020929-5 |
| title | Asymptotic methods for ordinary differential equations |
| title_auth | Asymptotic methods for ordinary differential equations |
| title_exact_search | Asymptotic methods for ordinary differential equations |
| title_full | Asymptotic methods for ordinary differential equations by R. P. Kuzmina |
| title_fullStr | Asymptotic methods for ordinary differential equations by R. P. Kuzmina |
| title_full_unstemmed | Asymptotic methods for ordinary differential equations by R. P. Kuzmina |
| title_short | Asymptotic methods for ordinary differential equations |
| title_sort | asymptotic methods for ordinary differential equations |
| topic | Differential equations Asymptotic theory Asymptotische Methode (DE-588)4287476-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Differential equations Asymptotic theory Asymptotische Methode Gewöhnliche Differentialgleichung |
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