Perturbation methods for differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2003
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 354 S. graph. Darst. |
| ISBN: | 3764341890 0817641890 |
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| 245 | 1 | 0 | |a Perturbation methods for differential equations |c Bhimsen K. Shivamoggi |
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| 650 | 4 | |a Perturbation (Mathématiques) | |
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| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
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Record in the Search Index
| _version_ | 1804129807883042816 |
|---|---|
| adam_text | IMAGE 1
BHIMSEN K. SHIVAMOGGI
PERTURBATION METHODS
FOR DIFFERENTIAL EQUATIONS
BIRKHAEUSER BOSTON * BASEL * BERLIN
IMAGE 2
TABLE OF CONTENTS
PREFACE XI
CHAPTER 1 ASYMPTOTIC SERIES AND EXPANSIONS 1
1.1 INTRODUCTION 1
1.2 TAYLOR SERIES EXPANSIONS 2
1.3 GAUGE FUNCTIONS 2
1.4 ASYMPTOTIC SERIES AND EXPANSIONS 4
1.5 ASYMPTOTIC SOLUTIONS OF DIFFERENTIAL EQUATIONS 10
1.6 EXERCISES 11
CHAPTER 2 REGULAER PERTURBATION METHODS 13
2.1 INTRODUCTION 13
2.2 ALGEBRAIC EQUATIONS 14
2.3 ORDINARY DIFFERENTIAL EQUATIONS 22
2.4 PARTIAL DIFFERENTIAL EQUATIONS . 29
2.5 APPLICATIONS TO FLUID DYNAMICS: DECAY OF A LINE VORTEX 31
2.6 EXERCISES 33
2.7 APPENDIX. REVIEW OF PARTIAL DIFFERENTIAL EQUATIONS 35
AI. TRANSFORMATION TO CANONICAL FORMS 35
IMAGE 3
VI CONTENTS
CHAPTER 3 THE METHOD OF STRAINED COORDINATES/PARAMETERS 41
3.1 INTRODUCTION 41
3.2 POINCARE-LINDSTEDT-LIGHTHILL METHOD OF PERTURBED EIGENVALUES 42
3.3 EIGENFUNCTION EXPANSION METHOD 52
3.4 LIGHTHILL S METHOD OF SHIFTING SINGULARITIES 55
3.5 PRITULO S METHOD OFRENORMALIZATION 59
3.6 WAVE PROPAGATION IN AN INHOMOGENEOUS MEDIUM 63
3.7 APPLICATIONS TO SOLID MECHANICS: NONLINEAR BUECKLING OF ELASTIC
COLUMNS 65
3.8 APPLICATIONS TO FLUID DYNAMICS 71
3.8.1 NONLINEAR HYPERBOLIC WAVES IN A GAS 71
3.8.2 RAYLEIGH-TAYLOR INSTABILITY OF SUPERPOSED FLUIDS 75
3.9 APPLICATIONS TO PLASMA PHYSICS . 82
3.9.1 NONLINEAR WAVES IN AN ELECTRON-PLASMA 82
3.9.2 RAYLEIGH-TAYLOR INSTABILITY OF A PLASMA IN A MAGNETIC FIELD 84
3.10 LIMITATIONS OF THE METHOD OF STRAINED PARAMETERS 91
3.11 EXERCISES 93
3.12 APPENDIX 1. FREDHOLM S ALTERNATIVE THEOREM 95
3.13 APPENDIX 2. FLOQUET THEORY 97
3.14 APPENDIX 3. BIFURCATION THEORY 107
CHAPTER 4 METHOD OF AVERAGING 113
4.1 INTRODUCTION 113
4.2 KRYLOV-BOGOLIUBOV METHOD OF AVERAGING 114
4.3 KRYLOV-BOGOLIUBOV-MITROPOLSKI GENERALIZED METHOD OF AVERAGING 118
4.4 WHITHAM S AVERAGED LAGRANGIAN METHOD 122
4.5 HAMILTONIAN PERTURBATION METHOD 125
4.5.1 SYSTEMS WITH CONSTANT PARAMETERS 125
4.5.2 SYSTEMS WITH SLOWLY-VARYING PARAMETERS 130
4.6 APPLICATIONS TO FLUID DYNAMICS: NONLINEAR EVOLUTION OF
IMAGE 4
CONTENTS / V LL
MODULATED GRAVITY WAVE PACKET ON THE SURFACE OF A FLUID 135
4.7 EXERCISES 139
4.8 APPENDIX 1. REVIEW OF CALCULUS OF VARIATIONS 141
A1.1 FUNCTIONALS WITH SECOND-ORDER DERIVATIVES 141
AI .2 FUNCTIONALS WITH HIGHER-ORDER DERIVATIVES 144
AI .3 FUNCTIONALS WITH SEVERAL INDEPENDENT VARIABLES.... 145
4.9 APPENDIX 2. HAMILTON-JACOBI THEORY 148
A2.1 HAMILTON S EQUATIONS 148
A2.2 CANONICAL TRANSFORMATIONS 150
A2.3 HAMILTON-JACOBI EQUATION 152
A2.4 ACTION-ANGLE VARIABLES 153
CHAPTER 5 THE METHOD OF MATCHED ASYMPTOTIC EXPANSIONS 155
5.1 INTRODUCTION 155
5.2 PHYSICAL MOTIVATION 155
5.3 THE INNER AND OUTER EXPANSIONS 158
5.4 HYPERBOLIC EQUATIONS 166
5.5 ELLIPTIC EQUATIONS 176
5.6 PARABOLIC EQUATIONS 179
5.7 INTERIOR LAYERS 181
5.8 LATTA S METHOD OFCOMPOSITE EXPANSIONS 185
5.9 TUMING POINT PROBLEMS 190
5.9.1 JWKB APPROXIMATION 190
5.9.2 SOLUTION NEAR THE TURNING POINT 194
5.9.3 LANGER S METHOD 197
5.10 APPLICATIONS TO FLUID DYNAMICS: BOUNDARY-LAYER FLOW PAST A FIAT
PLATE 199
5.10.1 THE OUTER EXPANSION 199
5.10.2 THE INNER EXPANSION 201
5.10.3 FLOW DUE TO DISPLACEMENT THICKNESS 206
IMAGE 5
VIII
CONTENTS
5.11 EXERCISES 207
5.12 APPENDIX 1. INITIAL-VALUE PROBLEM FOR PARTIAL DIFFERENTIAL
EQUATIONS.... 209
5.13 APPENDIX 2. REVIEW OF NONLINEAR HYPERBOLIC EQUATIONS . 211
CHAPTER 6 METHOD OF MULTIPLE SCALES 219
6.1 INTRODUCTION 219
6.2 DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS 219
6.3 STRUBLE S METHOD 243
6.4 DIFFERENTIAL EQUATIONS WITH SLOWLY VARYING COEFFICIENTS 252
6.5 GENERALIZED MULTIPLE-SCALE METHOD ,. 262
6.6 APPLICATIONS TO SOLID MECHANICS: DYNAMIC BUECKLING OF A THIN ELASTIC
PLATE 265
6.7 APPLICATIONS TO FLUID DYNAMICS 273
6.7.1 THE PROBLEM OF AERODYNAMICALLY GENERATED SOUND 273
6.7.2 MATHEMATICALFORMALIZATIONOFLIGHTHILL S , THEORY OF AERODYNAMICALLY
GENERATED SOUND 276
6.7.3 NONLINEAR SHALLOW WATER WAVES 281
6.7.3(A) GOVERNING EQUATIONS 282
6.7.3(B) KORTEWEG-DEVRIES EQUATION 284
6.7.3(C) SOLITARY WAVES , 286
6.7.3(D) STOKES WAVES 288
6.7.3(E) PERTURBED SOLITARY WAVE PROPAGATION 290
6.7.3(F) WAVE MODULATION AND NONLINEAR SCHROEDINGER EQUATION 295
6.7.3(G) LONG-TIME EVOLUTION OF THE MODULATION 299
6.7.3(H) SECOND-HARMONIC RESONANCE 303
6.8 APPLICATIONS TO PLASMA PHYSICS 307
6.8.1 NONLINEAR LONGITUDINAL WAVES IN A HOT ELECTRON-PLASMA 307
6.8.2 LON-ACOUSTIC SOLITARY WAVES IN AN INHOMOGENEOUS PLASMA 310
6.9 EXERCISES 316
IMAGE 6
CONTENTS IX
CHAPTER 7 MISCELLANEOUS PERTURBATION METHODS 319
7.1 A QUANTUM-FIELD-THEORETIC PERTURBATIVE PROCEDURE 319
7.1.1 BLASIUS EQUATION 320
7.2 A PERTURBATION METHOD FOR LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS
322
7.2.1 APPLICATION TO WAVE PROPAGATION IN A RANDOM MEDIUM 325
7.2.2 RENORMALIZATION PROCEDURE 327
7.2.2(A) EXACT SOLUTION 327
7.2.2(B) PERTURBATIVE SOLUTION 328
7.2.2(C) RENORMALIZED SOLUTION 329
7.3 EXERCISES 333
REFERENCES 335
ANSWERS TO SELECTED PROBLEMS 343
INDEX S . 347
PERMISSIONS 353
|
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| language | English |
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| spelling | Shivamoggi, Bhimsen K. 1950- Verfasser (DE-588)124325823 aut Perturbation methods for differential equations Bhimsen K. Shivamoggi Boston [u.a.] Birkhäuser 2003 XIV, 354 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Perturbation (Mathématiques) Équations aux dérivées partielles - Solutions numériques Équations différentielles - Solutions numériques Differential equations Numerical solutions Differential equations, Partial Numerical solutions Perturbation (Mathematics) Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Störungstheorie (DE-588)4128420-3 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Störungstheorie (DE-588)4128420-3 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010188757&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shivamoggi, Bhimsen K. 1950- Perturbation methods for differential equations Perturbation (Mathématiques) Équations aux dérivées partielles - Solutions numériques Équations différentielles - Solutions numériques Differential equations Numerical solutions Differential equations, Partial Numerical solutions Perturbation (Mathematics) Differentialgleichung (DE-588)4012249-9 gnd Störungstheorie (DE-588)4128420-3 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4128420-3 |
| title | Perturbation methods for differential equations |
| title_auth | Perturbation methods for differential equations |
| title_exact_search | Perturbation methods for differential equations |
| title_full | Perturbation methods for differential equations Bhimsen K. Shivamoggi |
| title_fullStr | Perturbation methods for differential equations Bhimsen K. Shivamoggi |
| title_full_unstemmed | Perturbation methods for differential equations Bhimsen K. Shivamoggi |
| title_short | Perturbation methods for differential equations |
| title_sort | perturbation methods for differential equations |
| topic | Perturbation (Mathématiques) Équations aux dérivées partielles - Solutions numériques Équations différentielles - Solutions numériques Differential equations Numerical solutions Differential equations, Partial Numerical solutions Perturbation (Mathematics) Differentialgleichung (DE-588)4012249-9 gnd Störungstheorie (DE-588)4128420-3 gnd |
| topic_facet | Perturbation (Mathématiques) Équations aux dérivées partielles - Solutions numériques Équations différentielles - Solutions numériques Differential equations Numerical solutions Differential equations, Partial Numerical solutions Perturbation (Mathematics) Differentialgleichung Störungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010188757&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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