Symmetry and integration methods for differential equations:
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| Previous Title: | Bluman, George W. Symmetries and differential equations |
|---|---|
| Main Authors: | , |
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Edition: | [2. ed.] |
| Series: | Applied mathematical sciences
154 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 419 S. graph. Darst. |
| ISBN: | 0387986545 |
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Record in the Search Index
| _version_ | 1804129380267458560 |
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| adam_text | GEORGE W. BLUMAN STEPHEN C. ANCO SYMMETRY AND INTEGRATION METHODS FOR
DIFFERENTIAL EQUATIONS WITH 18 ILLUSTRATIONS SPRINGER CONTENTS PREFACE V
INTRODUCTION 1 1 DIMENSIONAL ANALYSIS, MODELING, AND INVARIANCE 5 1.1
INTRODUCTION 5 1.2 DIMENSIONAL ANALYSIS: BUCKINGHAM PI-THEOREM 5 1.2.1
ASSUMPTIONS BEHIND DIMENSIONAL ANALYSIS 5 1.2.2 CONCLUSIONS FROM
DIMENSIONAL ANALYSIS 7 1.2.3 PROOF OF THE BUCKINGHAM PI-THEOREM 8 1.2.4
EXAMPLES . 11 1.3 APPLICATION OF DIMENSIONAL ANALYSIS TO PDES 16 1.3.1
EXAMPLES 17 1.4 GENERALIZATION OF DIMENSIONAL ANALYSIS: INVARIANCE OF
PDES UNDER SCALINGS OF VARIABLES 25 1.5 DISCUSSION 31 2 LIE GROUPS OF
TRANSFORMATIONS AND INFINITESIMAL TRANSFORMATIONS 33 2.1 INTRODUCTION 33
2.2 LIE GROUPS OF TRANSFORMATIONS 34 2.2.1 GROUPS 34 2.2.2 EXAMPLES OF
GROUPS 34 2.2.3 GROUP OF TRANSFORMATIONS 36 2.2.4 ONE-PARAMETER LIE
GROUP OF TRANSFORMATIONS 36 2.2.5 EXAMPLES OF ONE-PARAMETER LIE GROUPS
OF TRANSFORMATIONS 37 2.3 INFINITESIMAL TRANSFORMATIONS 38 2.3.1 FIRST
FUNDAMENTAL THEOREM OF LIE 39 2.3.2 EXAMPLES ILLUSTRATING LIE S FIRST
FUNDAMENTAL THEOREM 41 2.3.3 INFINITESIMAL GENERATORS 42 2.3.4 INVARIANT
FUNCTIONS 46 2.3.5 CANONICAL COORDINATES 47 2.3.6 EXAMPLES OF SETS OF
CANONICAL COORDINATES 49 2.4 POINT TRANSFORMATIONS AND EXTENDED
TRANSFORMATIONS (PROLONGATIONS) 52 2.4.1 EXTENDED GROUP OF POINT
TRANSFORMATIONS: ONE DEPENDENT AND ONE INDEPENDENT VARIABLE 53 VIII
CONTENTS 2.4.2 EXTENDED INFINITESIMAL TRANSFORMATIONS: ONE DEPENDENT AND
ONE INDEPENDENT VARIABLE 60 2.4.3 EXTENDED TRANSFORMATIONS: ONE
DEPENDENT AND N INDEPENDENT VARIABLES 62 2.4.4 EXTENDED INFINITESIMAL
TRANSFORMATIONS: ONE DEPENDENT AND N INDEPENDENT VARIABLES 65 2.4.5
EXTENDED TRANSFORMATIONS AND EXTENDED INFINITESIMAL TRANSFORMATIONS: M
DEPENDENT AND N INDEPENDENT VARIABLES 68 2.5 MULTIPARAMETER LIE GROUPS
OF TRANSFORMATIONS AND LIE ALGEBRAS 72 2.5.1 R-PARAMETER LIE GROUPS OF
TRANSFORMATIONS 73 2.5.2 LIE ALGEBRAS 77 2.5.3 EXAMPLES OF LIE ALGEBRAS
79 2.5.4 SOLVABLE LIE ALGEBRAS 82 2.6 MAPPINGS OF CURVES AND SURFACES 85
2.6.1 INVARIANT SURFACES, INVARIANT CURVES, INVARIANT POINTS 85 2.6.2
MAPPINGS OF CURVES 89 2.6.3 EXAMPLES OF MAPPINGS OF CURVES 90 2.6.4
MAPPINGS OF SURFACES 91 2.7 LOCAL TRANSFORMATIONS 92 2.7.1 POINT
TRANSFORMATIONS 92 2.7.2 CONTACT AND HIGHER-ORDER TRANSFORMATIONS 94
2.7.3 EXAMPLES OF LOCAL TRANSFORMATIONS 95 2.8 DISCUSSION 97 3 ORDINARY
DIFFERENTIAL EQUATIONS (ODES) 101 3.1 INTRODUCTION 101 3.1.1 ELEMENTARY
EXAMPLES 102 3.2 FIRST-ORDER ODES 106 3.2.1 CANONICAL COORDINATES 107
3.2.2 INTEGRATING FACTORS 109 3.2.3 MAPPINGS OF SOLUTION CURVES 110
3.2.4 DETERMINING EQUATION FOR SYMMETRIES OF A FIRST-ORDER ODE 112 3.2.5
DETERMINATION OF FIRST-ORDER ODES INVARIANT UNDER A GIVEN GROUP 114 3.3
INVARIANCE OF SECOND-AND HIGHER-ORDER ODES UNDER POINT SYMMETRIES 121
3.3.1 REDUCTION OF ORDER THROUGH CANONICAL COORDINATES 122 3.3.2
REDUCTION OF ORDER THROUGH DIFFERENTIAL INVARIANTS 124 3.3.3 EXAMPLES OF
REDUCTION OF ORDER 126 3.3.4 DETERMINING EQUATIONS FOR POINT SYMMETRIES
OF AN TH-ORDERODE 132 3.3.5 DETERMINATION OF TH-ORDER ODES INVARIANT
UNDER A GIVEN GROUP 137 CONTENTS IX 3.4 REDUCTION OF ORDER OF ODES UNDER
MULTIPARAMETER LIE GROUPS OF POINT TRANSFORMATIONS 141 3.4.1 INVARIANCE
OF A SECOND-ORDER ODE UNDER A TWO-PARAMETER LIE GROUP 141 3.4.2
INVARIANCE OF AN NTH-ORDER ODE UNDER A TWO-PARAMETER LIE GROUP 145 3.4.3
INVARIANCE OF AN WTH-ORDER ODE UNDER AN R-PARAMETER LIE GROUP WITH A
SOLVABLE LIE ALGEBRA 150 3.4.4 INVARIANCE OF AN OVERDETERMINED SYSTEM OF
ODES UNDER AN R-PARAMETER LIE GROUP WITH A SOLVABLE LIE ALGEBRA 159 3.5
CONTACT SYMMETRIES AND HIGHER-ORDER SYMMETRIES 165 3.5.1 DETERMINING
EQUATIONS FOR CONTACT SYMMETRIES AND HIGHER-ORDER SYMMETRIES 167 3.5.2
EXAMPLES OF CONTACT SYMMETRIES AND HIGHER-ORDER SYMMETRIES 169 3.5.3
REDUCTION OF ORDER USING POINT SYMMETRIES IN CHARACTERISTIC FORM 175
3.5.4 REDUCTION OF ORDER USING CONTACT SYMMETRIES AND HIGHER-ORDER
SYMMETRIES 179 3.6 FIRST INTEGRALS AND REDUCTION OF ORDER THROUGH
INTEGRATING FACTORS 185 3.6.1 FIRST-ORDER ODES 187 3.6.2 DETERMINING
EQUATIONS FOR INTEGRATING FACTORS OF SECOND-ORDER ODES 191 3.6.3 FIRST
INTEGRALS OF SECOND-ORDER ODES 196 3.6.4 DETERMINING EQUATIONS FOR
INTEGRATING FACTORS OF THIRD- AND HIGHER-ORDER ODES 208 3.6.5 EXAMPLES
OF FIRST INTEGRALS OF THIRD- AND HIGHER-ORDER ODES 221 3.7 FUNDAMENTAL
CONNECTIONS BETWEEN INTEGRATING FACTORS AND SYMMETRIES 232 3.7.1
ADJOINT-SYMMETRIES 233 3.7.2 ADJOINT INVARIANCE CONDITIONS AND
INTEGRATING FACTORS 236 3.7.3 EXAMPLES OF FINDING ADJOINT-SYMMETRIES AND
INTEGRATING FACTORS 238 3.7.4 NOETHER S THEOREM, VARIATIONAL SYMMETRIES,
AND INTEGRATING FACTORS 245 3.7.5 COMPARISON OF CALCULATIONS OF
SYMMETRIES, ADJOINT-SYMMETRIES, AND INTEGRATING FACTORS 251 3.8 DIRECT
CONSTRUCTION OF FIRST INTEGRALS THROUGH SYMMETRIES AND
ADJOINT-SYMMETRIES 255 3.8.1 FIRST INTEGRALS FROM SYMMETRY AND
ADJOINT-SYMMETRY PAIRS 256 3.8.2 FIRST INTEGRALS FROM A WRONSKIAN
FORMULA USING SYMMETRIES OR ADJOINT-SYMMETRIES 262 3.8.3 FIRST INTEGRALS
FOR SELF-ADJOINT ODES 270 X CONTENTS 3.9 APPLICATIONS TO BOUNDARY VALUE
PROBLEMS 275 3.10 INVARIANT SOLUTIONS 279 3.10.1 INVARIANT SOLUTIONS FOR
FIRST-ORDER ODES: SEPARATRICES AND ENVELOPES 284 3.11 DISCUSSION 290 4
PARTIAL DIFFERENTIAL EQUATIONS (PDES) 297 4.1 INTRODUCTION 297 4.1.1
INVARIANCE OFAPDE 297 4.1.2 ELEMENTARY EXAMPLES 299 4.2 INVARIANCE FOR
SCALAR PDES 303 4.2.1 INVARIANT SOLUTIONS 303 4.2.2 DETERMINING
EQUATIONS FOR SYMMETRIES OF A #TH-ORDER PDE 305 4.2.3 EXAMPLES 310 4.3
INVARIANCE FOR A SYSTEM OF PDES 330 4.3.1 INVARIANT SOLUTIONS 331 4.3.2
DETERMINING EQUATIONS FOR SYMMETRIES OF A SYSTEM OF PDES 333 4.3.3
EXAMPLES 335 4.4 APPLICATIONS TO BOUNDARY VALUE PROBLEMS 351 4.4.1
FORMULATION OF INVARIANCE OF A BOUNDARY VALUE PROBLEM FOR A SCALAR PDE
353 4.4.2 INCOMPLETE INVARIANCE FOR A LINEAR SCALAR PDE 369 4.4.3
INCOMPLETE INVARIANCE FOR A LINEAR SYSTEM OF PDES 379 4.5 DISCUSSION 387
REFERENCES 391 AUTHOR INDEX 401 SUBJECT INDEX 405
|
| any_adam_object | 1 |
| author | Bluman, George W. 1943- Anco, Stephen C. |
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| bvnumber | BV014603508 |
| classification_rvk | SK 500 SK 920 |
| ctrlnum | (OCoLC)634855284 (DE-599)BVBBV014603508 |
| discipline | Mathematik |
| edition | [2. ed.] |
| format | Book |
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| indexdate | 2024-07-09T19:04:13Z |
| institution | BVB |
| isbn | 0387986545 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009926760 |
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| physical | X, 419 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Bluman, George W. 1943- Verfasser (DE-588)143539035 aut Symmetry and integration methods for differential equations George W. Bluman ; Stephen C. Anco [2. ed.] Berlin [u.a.] Springer 2002 X, 419 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 154 Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Numerisches Verfahren (DE-588)4128130-5 s Lie-Gruppe (DE-588)4035695-4 s DE-604 Anco, Stephen C. Verfasser aut 1. Auflage Bluman, George W. Symmetries and differential equations Applied mathematical sciences 154 (DE-604)BV000005274 154 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009926760&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bluman, George W. 1943- Anco, Stephen C. Symmetry and integration methods for differential equations Applied mathematical sciences Lie-Gruppe (DE-588)4035695-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4128130-5 (DE-588)4012249-9 |
| title | Symmetry and integration methods for differential equations |
| title_auth | Symmetry and integration methods for differential equations |
| title_exact_search | Symmetry and integration methods for differential equations |
| title_full | Symmetry and integration methods for differential equations George W. Bluman ; Stephen C. Anco |
| title_fullStr | Symmetry and integration methods for differential equations George W. Bluman ; Stephen C. Anco |
| title_full_unstemmed | Symmetry and integration methods for differential equations George W. Bluman ; Stephen C. Anco |
| title_old | Bluman, George W. Symmetries and differential equations |
| title_short | Symmetry and integration methods for differential equations |
| title_sort | symmetry and integration methods for differential equations |
| topic | Lie-Gruppe (DE-588)4035695-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Lie-Gruppe Numerisches Verfahren Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009926760&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
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