Introduction to asymptotic methods:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL
Chapman & Hall/CRC
2006
|
| Series: | CRC series: Modern mechanics and mathematics
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 233-242) and index |
| Physical Description: | XVIII, 251 S. graph. Darst. |
| ISBN: | 1584886773 9781584886778 |
Staff View
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| adam_text | INTRODUCTION TO ASYMPTOTIC METHODS JAN AWREJCEWICZ VADIM A. KRYSKO
^L|CHAPMAN S. HALL/CRC M M TAYLOR SI FRANCIS GROUP BOCA RATON LONDON NEW
YORK CHAPMAN & HALL/CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS CROUP, AN
INFORMA BUSINESS CONTENTS INTRODUCTION XV 1 ELEMENTS OF MATHEMATICAL
MODELING 1 1.1 STRUCTURE OF A MATHEMATICAL MODEL 1 1.2 EXAMPLES OF
REDUCING PROBLEMS TO A DIMENSIONLESS FORM . . . 3 1.3 MATHEMATICAL MODEL
ADEQUACY AND PROPERTIES. REGULAER AND SIN- GULAR PERTURBATIONS 7 2
EXPANSION OF FUNCTIONS AND MATHEMATICAL METHODS 9 2.1 EXPANSIONS OF
ELEMENTARY FUNCTIONS INTO POWER SERIES . . . . 9 2.1.1 NEWTON S BINOMIAL
9 2.1.2 TAYLOR AND MACLAURIN SERIES 10 2.1.3 ESTIMATION OF APPROXIMATING
FUNCTIONS VALUES 13 2.1.4 ESTIMATION OF APPROXIMATING VALUES OF DEFINITE
INTEGRALS 14 2.1.5 APPROXIMATING SOLUTION OF CAUCHY PROBLEM FOR ORDINARY
DIFFERENTIAL EQUATIONS 14 2.2 MATHEMATICAL METHODS OF PERTURBATIONS 16
2.2.1 PERTURBATION ALONG A PARAMETER AND COORDINATES. CLAS- SICAL METHOD
OF A SMALL PARAMETER 16 2.2.2 COMPARISON OF INFMITELY SMALL AND
INFINITELY LARGE FUNC- TIONS. SCALING FUNCTIONS. MAGNITUDE ORDER
QUANTITIES . 17 2.2.3 ASYMPTOTICAL SEQUENCES AND DECOMPOSITIONS 22 2.2.4
NONUNIFORM ASYMPTOTIC DECOMPOSITIONS 25 2.2.5 OPERATIONS ON ASYMPTOTIC
DECOMPOSITIONS 26 2.2.6 ASYMPTOTIC SERIES. COMPARISON OF ASYMPTOTIC AND
CON- VERGENT SERIES. ADVANTAGES OF APPLICATION OF ASYMPTOTIC SERIES AND
DECOMPOSITIONS 29 EXERCISES 32 3 REGULAER AND SINGULAR PERTURBATIONS 35
3.1 INTRODUCTION. ASYMPTOTIC APPROXIMATION WITH RESPECT TO A PA- RAMETER
36 3.2 NONUNIFORMITIES OF A CLASSICAL PERTURBATION APPROACH 40 3.3
METHOD OF ELONGATED PARAMETERS 43 3.4 METHOD OF DEFORMED VARIABLES 47
3.5 METHOD OF SCALING AND FUELL APPROXIMATION 52 3.5.1 DEFORMATION OF ONE
INDEPENDENT VARIABLE 53 V VI 3.5.2 DEFORMATION OF TWO INDEPENDENT
VARIABLES 55 3.5.3 METHOD OF FUELL APPROXIMATION 57 3.6 MULTIPLE SCALE
METHODS 58 3.6.1 INTRODUCTION 58 3.6.2 DERIVATIVE DECOMPOSITION ALONG
ONE AND TWO VARIABLES 62 3.6.3 APPLICATION TO THE PROBLEMS OF VIBRATIONS
63 3.7 VARIATIONS OF ARBITRARY CONSTANTS 68 3.8 AVERAGING METHODS 72
3.8.1 METHODS OF VAN DER POL AND KRYLOV-BOGOLUBOV-MITRO- POLSKIY (KBM)
72 3.8.2 DUFFING S PROBLEM AND THE AVERAGING PROCEDURE .... 75 3.9
MATCHING ASYMPTOTIC DECOMPOSITIONS 77 3.9.1 FUNDAMENTAL NOTIONS AND
TERMINOLOGY 77 3.9.2 EXAMPLE WITH A BOUNDARY LAYER 82 3.9.3 FUNDAMENTAL
RULES AND ORDER OF MATCHING 84 3.9.4 CONSTRUCTION OF MATCHED ASYMPTOTIC
EXPANSION .... 87 3.9.5 EXAMPLE WITH A SINGULARITY 88 3.9.6 ON THE
CHOICE OF INTERNAL VARIABLES 90 3.10 ON THE SOURCES OF NONUNIFORMITIES
92 3.11 ON THE INFLUENCE OF INITIAL CONDITIONS 94 3.12 ANALYSIS OF
STRONGLY NONLINEAR DYNAMICAL PROBLEMS 97 3.13 A FEW PERTURBATION
PARAMETERS 108 EXERCISES 111 4 WAVE-IMPACT PROCESSES 115 4.1 DEFINITION
OF A CYLINDER-LIKE PISTON WAVE 115 4.1.1 DEFINING THE PROBLEM, ITS
SOLUTION AND ANALYSIS .... 115 4.1.2 NONLINEAR SOLUTION IN THE VICINITY
OF THE PISTON .... 118 4.1.3 NONLINEAR SOLUTION IN THE VICINITY OF THE
FRONT OF THE IMPACT WAVE 119 4.1.4 METHODS OF STRAINED COORDINATES AND
RENORMALIZATION . 124 4.1.5 EFFECTIVENESS OF VARIOUS ASYMPTOTIC METHODS
130 4.2 ONE-DIMENSIONAL NONSTATIONARY NONLINEAR WAVES 130 4.2.1
FORMULATION OF THE PROBLEM AND ITS SOLUTION 130 4.2.2 RENORMALIZATION
METHOD AND SINGULARITIES 133 4.2.3 ANALYTICAL METHOD OF CHARACTERISTICS
134 4.2.4 MULTIPLE SCALES METHOD 137 5 PADE APPROXIMATIONS 141 5.1
DETERMINATION AND CHARACTERISTICS OF PADE APPROXIMATIONS . 141 5.2
APPLICATION OF PADE APPROXIMATIONS 144 5.2.1 SIMPLE EXAMPLES 144 5.2.2
SUPERSONIC FLOW ROUND A THIN CONE IN CIRCUMSONIC REGIME 145 5.2.3
DAMPING OF THE BALL-SHAPED WAVES OF PRESSURE IN A FREE SPACE AND IN A
TUBE 146 VII 5.2.4 ANALYSIS OF THE BLOW-UP PHENOMENON 149 5.2.5
HOMOCLINIC ORBITS 158 5.2.6 VIBRATIONS OF NONLINEAR SYSTEM WITH
NONLINEARITY CLOSE TO SIGN (X) 160 EXERCISES 163 6 AVERAGING OF RIBBED
PLATES 165 6.1 AVERAGING IN THE THEORY OF RIBBED PLATES 165 6.2
KANTOROVICH-VLASOV-TYPE METHODS 169 6.2.1 KANTOROWICH-VLASOV METHOD
(KVM) 170 6.2.2 VINDINER METHOD (VM) 170 6.2.3 METHOD OF VARIATIONAL
ITERATIONS (MVI) 171 6.2.4 AGRANOWSKY-BAGLAY-SMIRNOV METHOD (ABSM) . . .
. 171 6.2.5 COMBINED METHOD (CM) 172 6.2.6 KANTOROVICH-VLASOV METHOD
WITH THE AMENDMENT . . . 173 6.2.7 VINDINER METHOD WITH THE AMENDMENT
173 6.2.8 VINDINER METHOD AND VARIATIONAL ITERATIONS 173 6.3 TRANSVERSE
VIBRATIONS OF RECTANGULAR PLATES 174 6.4 DEFLECTIONS OF RECTANGULAR
PLATES 187 7 CHAOS FORESIGHT 191 7.1 THE ANALYZED SYSTEM 192 7.2
MELNIKOV-GRUENDLER S APPROACH 194 7.3 MELNIKOV-GRUENDLER FUNCTION 195
7.4 NUMERICAL RESULTS 199 8 CONTINUOUS APPROXIMATION OF DISCONTINUOUS
SYSTEMS 203 8.1 AN ILLUSTRATIVE EXAMPLE 203 8.2 HIGHER DIMENSIONAL
SYSTEMS 208 9 NONLINEAR DYNAMICS OF A SWINGING OSCILLATOR 217 9.1
PARAMETRICAL FORM OF CANONICAL TRANSFORMATIONS 218 9.2 FUNCTION
DERIVATIVE 218 9.3 INVARIANT NORMALIZATION OF HAMILTONIANS 220 9.4
ALGORITHM OF INVARIANT NORMALIZATION WITH THE HELP OF PARAME- TRIC
TRANSFORMATIONS 221 9.5 ALGORITHM OF INVARIANT NORMALIZATION FOR
ASYMPTOTICAL DETERMI- NATION OF THE POINCARE SERIES 224 9.6 EXAMPLES OF
ASYMPTOTICAL SOLUTIONS 225 9.7 A SWINGING OSCILLATOR 228 9.8 NORMAL FORM
230 9.9 NORMAL FORM INTEGRAL 231 REFERENCES 233 2VZ XAPUJ IUA
|
| adam_txt |
INTRODUCTION TO ASYMPTOTIC METHODS JAN AWREJCEWICZ VADIM A. KRYSKO
^L|CHAPMAN S. HALL/CRC M M TAYLOR SI FRANCIS GROUP BOCA RATON LONDON NEW
YORK CHAPMAN & HALL/CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS CROUP, AN
INFORMA BUSINESS CONTENTS INTRODUCTION XV 1 ELEMENTS OF MATHEMATICAL
MODELING 1 1.1 STRUCTURE OF A MATHEMATICAL MODEL 1 1.2 EXAMPLES OF
REDUCING PROBLEMS TO A DIMENSIONLESS FORM . . . 3 1.3 MATHEMATICAL MODEL
ADEQUACY AND PROPERTIES. REGULAER AND SIN- GULAR PERTURBATIONS 7 2
EXPANSION OF FUNCTIONS AND MATHEMATICAL METHODS 9 2.1 EXPANSIONS OF
ELEMENTARY FUNCTIONS INTO POWER SERIES . . . . 9 2.1.1 NEWTON'S BINOMIAL
9 2.1.2 TAYLOR AND MACLAURIN SERIES 10 2.1.3 ESTIMATION OF APPROXIMATING
FUNCTIONS VALUES 13 2.1.4 ESTIMATION OF APPROXIMATING VALUES OF DEFINITE
INTEGRALS 14 2.1.5 APPROXIMATING SOLUTION OF CAUCHY PROBLEM FOR ORDINARY
DIFFERENTIAL EQUATIONS 14 2.2 MATHEMATICAL METHODS OF PERTURBATIONS 16
2.2.1 PERTURBATION ALONG A PARAMETER AND COORDINATES. CLAS- SICAL METHOD
OF A SMALL PARAMETER 16 2.2.2 COMPARISON OF INFMITELY SMALL AND
INFINITELY LARGE FUNC- TIONS. SCALING FUNCTIONS. MAGNITUDE ORDER
QUANTITIES . 17 2.2.3 ASYMPTOTICAL SEQUENCES AND DECOMPOSITIONS 22 2.2.4
NONUNIFORM ASYMPTOTIC DECOMPOSITIONS 25 2.2.5 OPERATIONS ON ASYMPTOTIC
DECOMPOSITIONS 26 2.2.6 ASYMPTOTIC SERIES. COMPARISON OF ASYMPTOTIC AND
CON- VERGENT SERIES. ADVANTAGES OF APPLICATION OF ASYMPTOTIC SERIES AND
DECOMPOSITIONS 29 EXERCISES 32 3 REGULAER AND SINGULAR PERTURBATIONS 35
3.1 INTRODUCTION. ASYMPTOTIC APPROXIMATION WITH RESPECT TO A PA- RAMETER
36 3.2 NONUNIFORMITIES OF A CLASSICAL PERTURBATION APPROACH 40 3.3
METHOD OF "ELONGATED" PARAMETERS 43 3.4 METHOD OF DEFORMED VARIABLES 47
3.5 METHOD OF SCALING AND FUELL APPROXIMATION 52 3.5.1 DEFORMATION OF ONE
INDEPENDENT VARIABLE 53 V VI 3.5.2 DEFORMATION OF TWO INDEPENDENT
VARIABLES 55 3.5.3 METHOD OF FUELL APPROXIMATION 57 3.6 MULTIPLE SCALE
METHODS 58 3.6.1 INTRODUCTION 58 3.6.2 DERIVATIVE DECOMPOSITION ALONG
ONE AND TWO VARIABLES 62 3.6.3 APPLICATION TO THE PROBLEMS OF VIBRATIONS
63 3.7 VARIATIONS OF ARBITRARY CONSTANTS 68 3.8 AVERAGING METHODS 72
3.8.1 METHODS OF VAN DER POL AND KRYLOV-BOGOLUBOV-MITRO- POLSKIY (KBM)
72 3.8.2 DUFFING'S PROBLEM AND THE AVERAGING PROCEDURE . 75 3.9
MATCHING ASYMPTOTIC DECOMPOSITIONS 77 3.9.1 FUNDAMENTAL NOTIONS AND
TERMINOLOGY 77 3.9.2 EXAMPLE WITH A BOUNDARY LAYER 82 3.9.3 FUNDAMENTAL
RULES AND ORDER OF MATCHING 84 3.9.4 CONSTRUCTION OF MATCHED ASYMPTOTIC
EXPANSION . 87 3.9.5 EXAMPLE WITH A SINGULARITY 88 3.9.6 ON THE
CHOICE OF INTERNAL VARIABLES 90 3.10 ON THE SOURCES OF NONUNIFORMITIES
92 3.11 ON THE INFLUENCE OF INITIAL CONDITIONS 94 3.12 ANALYSIS OF
STRONGLY NONLINEAR DYNAMICAL PROBLEMS 97 3.13 A FEW PERTURBATION
PARAMETERS 108 EXERCISES 111 4 WAVE-IMPACT PROCESSES 115 4.1 DEFINITION
OF A CYLINDER-LIKE PISTON WAVE 115 4.1.1 DEFINING THE PROBLEM, ITS
SOLUTION AND ANALYSIS . 115 4.1.2 NONLINEAR SOLUTION IN THE VICINITY
OF THE PISTON . 118 4.1.3 NONLINEAR SOLUTION IN THE VICINITY OF THE
FRONT OF THE IMPACT WAVE 119 4.1.4 METHODS OF STRAINED COORDINATES AND
RENORMALIZATION . 124 4.1.5 EFFECTIVENESS OF VARIOUS ASYMPTOTIC METHODS
130 4.2 ONE-DIMENSIONAL NONSTATIONARY NONLINEAR WAVES 130 4.2.1
FORMULATION OF THE PROBLEM AND ITS SOLUTION 130 4.2.2 RENORMALIZATION
METHOD AND SINGULARITIES 133 4.2.3 ANALYTICAL METHOD OF CHARACTERISTICS
134 4.2.4 MULTIPLE SCALES METHOD 137 5 PADE APPROXIMATIONS 141 5.1
DETERMINATION AND CHARACTERISTICS OF PADE APPROXIMATIONS . 141 5.2
APPLICATION OF PADE APPROXIMATIONS 144 5.2.1 SIMPLE EXAMPLES 144 5.2.2
SUPERSONIC FLOW ROUND A THIN CONE IN CIRCUMSONIC REGIME 145 5.2.3
DAMPING OF THE BALL-SHAPED WAVES OF PRESSURE IN A FREE SPACE AND IN A
TUBE 146 VII 5.2.4 ANALYSIS OF THE "BLOW-UP" PHENOMENON 149 5.2.5
HOMOCLINIC ORBITS 158 5.2.6 VIBRATIONS OF NONLINEAR SYSTEM WITH
NONLINEARITY CLOSE TO SIGN (X) 160 EXERCISES 163 6 AVERAGING OF RIBBED
PLATES 165 6.1 AVERAGING IN THE THEORY OF RIBBED PLATES 165 6.2
KANTOROVICH-VLASOV-TYPE METHODS 169 6.2.1 KANTOROWICH-VLASOV METHOD
(KVM) 170 6.2.2 VINDINER METHOD (VM) 170 6.2.3 METHOD OF VARIATIONAL
ITERATIONS (MVI) 171 6.2.4 AGRANOWSKY-BAGLAY-SMIRNOV METHOD (ABSM) . . .
. 171 6.2.5 COMBINED METHOD (CM) 172 6.2.6 KANTOROVICH-VLASOV METHOD
WITH THE AMENDMENT . . . 173 6.2.7 VINDINER METHOD WITH THE AMENDMENT
173 6.2.8 VINDINER METHOD AND VARIATIONAL ITERATIONS 173 6.3 TRANSVERSE
VIBRATIONS OF RECTANGULAR PLATES 174 6.4 DEFLECTIONS OF RECTANGULAR
PLATES 187 7 CHAOS FORESIGHT 191 7.1 THE ANALYZED SYSTEM 192 7.2
MELNIKOV-GRUENDLER'S APPROACH 194 7.3 MELNIKOV-GRUENDLER FUNCTION 195
7.4 NUMERICAL RESULTS 199 8 CONTINUOUS APPROXIMATION OF DISCONTINUOUS
SYSTEMS 203 8.1 AN ILLUSTRATIVE EXAMPLE 203 8.2 HIGHER DIMENSIONAL
SYSTEMS 208 9 NONLINEAR DYNAMICS OF A SWINGING OSCILLATOR 217 9.1
PARAMETRICAL FORM OF CANONICAL TRANSFORMATIONS 218 9.2 FUNCTION
DERIVATIVE 218 9.3 INVARIANT NORMALIZATION OF HAMILTONIANS 220 9.4
ALGORITHM OF INVARIANT NORMALIZATION WITH THE HELP OF PARAME- TRIC
TRANSFORMATIONS 221 9.5 ALGORITHM OF INVARIANT NORMALIZATION FOR
ASYMPTOTICAL DETERMI- NATION OF THE POINCARE SERIES 224 9.6 EXAMPLES OF
ASYMPTOTICAL SOLUTIONS 225 9.7 A SWINGING OSCILLATOR 228 9.8 NORMAL FORM
230 9.9 NORMAL FORM INTEGRAL 231 REFERENCES 233 2VZ XAPUJ IUA |
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| any_adam_object_boolean | 1 |
| author | Awrejcewicz, Jan 1952- |
| author_GND | (DE-588)120089122 (DE-588)124016731 |
| author_facet | Awrejcewicz, Jan 1952- |
| author_role | aut |
| author_sort | Awrejcewicz, Jan 1952- |
| author_variant | j a ja |
| building | Verbundindex |
| bvnumber | BV021746628 |
| callnumber-first | Q - Science |
| callnumber-label | QA372 |
| callnumber-raw | QA372 |
| callnumber-search | QA372 |
| callnumber-sort | QA 3372 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 520 |
| ctrlnum | (OCoLC)64511314 (DE-599)BVBBV021746628 |
| dewey-full | 515/.392 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.392 |
| dewey-search | 515/.392 |
| dewey-sort | 3515 3392 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV021746628 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:31:04Z |
| indexdate | 2024-07-09T20:43:06Z |
| institution | BVB |
| isbn | 1584886773 9781584886778 |
| language | English |
| lccn | 2006042615 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014959893 |
| oclc_num | 64511314 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XVIII, 251 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | CRC series: Modern mechanics and mathematics |
| series2 | CRC series: Modern mechanics and mathematics |
| spelling | Awrejcewicz, Jan 1952- Verfasser (DE-588)120089122 aut Introduction to asymptotic methods Jan Awrejcewicz, Vadim A. Krysko Boca Raton, FL Chapman & Hall/CRC 2006 XVIII, 251 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier CRC series: Modern mechanics and mathematics 5 Includes bibliographical references (p. 233-242) and index Singular perturbations (Mathematics) Differential equations Asymptotic theory Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Störungstheorie (DE-588)4128420-3 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Störungstheorie (DE-588)4128420-3 s Asymptotische Methode (DE-588)4287476-2 s DE-604 Krysʹko, Vadim A. 1937- Sonstige (DE-588)124016731 oth CRC series: Modern mechanics and mathematics 5 (DE-604)BV019670496 5 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014959893&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Awrejcewicz, Jan 1952- Introduction to asymptotic methods CRC series: Modern mechanics and mathematics Singular perturbations (Mathematics) Differential equations Asymptotic theory Asymptotische Methode (DE-588)4287476-2 gnd Störungstheorie (DE-588)4128420-3 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4287476-2 (DE-588)4128420-3 (DE-588)4020929-5 (DE-588)4151278-9 |
| title | Introduction to asymptotic methods |
| title_auth | Introduction to asymptotic methods |
| title_exact_search | Introduction to asymptotic methods |
| title_exact_search_txtP | Introduction to asymptotic methods |
| title_full | Introduction to asymptotic methods Jan Awrejcewicz, Vadim A. Krysko |
| title_fullStr | Introduction to asymptotic methods Jan Awrejcewicz, Vadim A. Krysko |
| title_full_unstemmed | Introduction to asymptotic methods Jan Awrejcewicz, Vadim A. Krysko |
| title_short | Introduction to asymptotic methods |
| title_sort | introduction to asymptotic methods |
| topic | Singular perturbations (Mathematics) Differential equations Asymptotic theory Asymptotische Methode (DE-588)4287476-2 gnd Störungstheorie (DE-588)4128420-3 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Singular perturbations (Mathematics) Differential equations Asymptotic theory Asymptotische Methode Störungstheorie Gewöhnliche Differentialgleichung Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014959893&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019670496 |
| work_keys_str_mv | AT awrejcewiczjan introductiontoasymptoticmethods AT krysʹkovadima introductiontoasymptoticmethods |