Differential-algebraic equations: a projector based analysis
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schriftenreihe: | Differential-algebraic equations forum, DAE-F
|
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=3931946&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025908136&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Lamour, René: Differential-Algebraic Equations: A Projector Based Analysis |
| Umfang: | XXVII, 649 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 3642275540 9783642275548 |
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| 245 | 1 | 0 | |a Differential-algebraic equations |b a projector based analysis |c René Lamour ; Roswitha März ; Caren Tischendorf |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XXVII, 649 S. |b graph. Darst. |c 235 mm x 155 mm | ||
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| 700 | 1 | |a Tischendorf, Caren |d 1969- |0 (DE-588)1036742962 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1819267304414773248 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
NOTATIONS XV
INTRODUCTION XIX
PART I PROJECTOR BASED APPROACH
1 LINEAR CONSTANT COEFFICIENT DAES 3
]. 1 REGULAR DAES AND THE WEIERSTRAB-KRONECKER FORM 3
1.2 PROJECTOR BASED DECOUPLING OF REGULAR DAES 10
1.2.1 ADMISSIBLE MATRIX SEQUENCES AND ADMISSIBLE PROJECTORS . . . . 10
1.2.2 DECOUPLING BY ADMISSIBLE PROJECTORS 23
1.2.3 COMPLETE DECOUPLING 30
1.2.4 HIERARCHY O F PROJECTOR SEQUENCES FOR CONSTANT MATRIX PENCILS 36
1.2.5 COMPRESSION TO A GENERALIZED WEIERSTRAB-KRONECKER FORM . . 37
1.2.6 ADMISSIBLE PROJECTORS FOR MATRIX PAIRS IN A GENERALIZED
WEIERSTRAB-KRONECKER FORM 4 1
1.3 TRANSFORMATION INVARIANCE 4 5
1.4 CHARACTERIZING MATRIX PENCILS BY ADMISSIBLE PROJECTORS 47
1.5 PROPERLY STATED LEADING TERM AND SOLUTION SPACE 50
1.6 NOTES AND REFERENCES 52
2 LINEAR DAES WITH VARIABLE COEFFICIENTS 57
2.1 PROPERLY STATED LEADING TERMS 58
2.2 ADMISSIBLE MATRIX FUNCTION SEQUENCES 6 0
2.2.1 BASICS 60
2.2.2 ADMISSIBLE PROJECTOR FUNCTIONS AND CHARACTERISTIC V A L U E S . .
. . 65 2.2.3 WIDELY ORTHOGONAL PROJECTOR FUNCTIONS 75
2.3 INVARIANTS UNDER TRANSFORMATIONS AND REFACTORIZATIONS 79
2.4 DECOUPLING REGULAR DAES 86
2.4.1 PRELIMINARY DECOUPLING REARRANGEMENTS 86
IX
HTTP://D-NB.INFO/1017779376
IMAGE 2
X C O N T E N T S
2.4.2 REGULARITY AND BASIC DECOUPLING OF REGULAR DAES 90
2.4.3 FINE AND COMPLETE DECOUPLINGS 104
2.4.3.1 INDEX-1 CASE 104
2.4.3.2 INDEX-2 CASE 106
2.4.3.3 GENERAL BENEFITS FROM FINE DECOUPLINGS 108
2.4.3.4 EXISTENCE O F FINE AND COMPLETE DECOUPLINGS I L L
2.5 HIERARCHY OF ADMISSIBLE PROJECTOR FUNCTION SEQUENCES FOR LINEAR DAES
117
2.6 FINE REGULAR DAES 118
2.6.1 FUNDAMENTAL SOLUTION MATRICES 119
2.6.2 CONSISTENT INITIAL VALUES AND FLOW STRUCTURE 123
2.6.3 STABILITY ISSUES 127
2.6.4 CHARACTERIZING ADMISSIBLE EXCITATIONS AND PERTURBATION INDEX 132
2.7 SPECIFICATIONS FOR REGULAR STANDARD FORM DAES 137
2.8 THE T-CANONICAL FORM 140
2.9 REGULARITY INTERVALS AND CRITICAL POINTS 146
2.10 STRANGENESS VERSUS TRACTABILITY 160
2.10.1 CANONICAL FORMS 160
2.10.2 STRANGENESS REDUCTION 164
2.10.3 PROJECTOR BASED REDUCTION 166
2.11 GENERALIZED SOLUTIONS 171
2.11.1 MEASURABLE SOLUTIONS 171
2.11.2 DISTRIBUTIONAL SOLUTIONS 173
2.12 NOTES AND REFERENCES 174
3 NONLINEAR DAES 183
3.1 BASIC ASSUMPTIONS AND NOTIONS 184
3.1.1 PROPERLY INVOLVED DERIVATIVE 184
3.1.2 CONSTRAINTS AND CONSISTENT INITIAL VALUES 187
3.1.3 LINEARIZATION 195
3.2 ADMISSIBLE MATRIX FUNCTION SEQUENCES AND ADMISSIBLE PROJECTOR
FUNCTIONS 198
3.3 REGULARITY REGIONS 208
3.4 TRANSFORMATION INVARIANCE 224
3.5 HESSENBERG FORM DAES OF ARBITRARY SIZE 229
3.6 DAES IN CIRCUIT SIMULATION 239
3.7 LOCAL SOLVABILITY 250
3.7.1 INDEX-1 DAES 251
3.7.2 INDEX-2 DAES 259
3.7.2.1 ADVANCED DECOUPLING O F LINEAR INDEX-2 DAES . . . . 2 5 9
3.7.2.2 NONLINEAR INDEX-2 DAES 261
3.7.2.3 INDEX REDUCTION STEP 268
3.8 ADVANCED LOCALIZATION O F REGULARITY: INCLUDING JET VARIABLES 272
3.9 OPERATOR SETTINGS 281
IMAGE 3
CONTENTS XI
3.9.1 LINEAR CASE 283
3.9.2 NONLINEAR CASE 287
3.10 A GLANCE AT THE STANDARD APPROACH VIA THE DERIVATIVE ARRAY AND
DIFFERENTIATION INDEX 290
3.11 USING STRUCTURAL PECULIARITIES TO EASE MODELS 300
3.12 REGULARITY REGIONS O F DAES WITH QUASI-PROPER LEADING TERMS 304
3.13 NOTES AND REFERENCES 307
PART II INDEX-1 DAES: ANALYSIS AND NUMERICAL TREATMENT
4 ANALYSIS 317
4.1 BASIC ASSUMPTIONS AND NOTIONS 317
4.2 STRUCTURE AND SOLVABILITY O F INDEX-1 DAES 320
4.3 CONSISTENT INITIAL VALUES 334
4.4 NOTES AND REFERENCES 336
5 NUMERICAL INTEGRATION 339
5.1 BASIC IDEA 340
5.2 METHODS APPLIED TO ODES AND DAES IN STANDARD FORM 345
5.2.1 BACKWARD DIFFERENTIATION FORMULA 345
5.2.2 RUNGE-KUTTA METHOD 346
5.2.3 GENERAL LINEAR METHOD 350
5.3 METHODS APPLIED TO DAES WITH A PROPERLY INVOLVED DERIVATIVE 352
5.3.1 BACKWARD DIFFERENTIATION FORMULA 352
5.3.2 RUNGE-KUTTA METHOD 353
5.3.3 GENERAL LINEAR METHOD 355
5.4 WHEN DO DECOUPLING AND DISCRETIZATION COMMUTE? 356
5.5 CONVERGENCE ON COMPACT INTERVALS AND ERROR ESTIMATIONS 361
5.5.1 BACKWARD DIFFERENTIATION FORMULA 361
5.5.2 IRK(DAE) METHOD 364
5.5.3 GENERAL LINEAR METHOD 369
5.6 NOTES AND REFERENCES 371
6 STABILITY ISSUES 375
6.1 PRELIMINARIES CONCERNING EXPLICIT ODES 375
6.2 CONTRACTIVE DAES AND B-STABLE RUNGE-KUTTA METHODS 378
6.3 DISSIPATIVITY 384
6.4 LYAPUNOV STABILITY 387
6.5 NOTES AND REFERENCES 394
PART III COMPUTATIONAL ASPECTS
7 COMPUTATIONAL LINEAR ALGEBRA ASPECTS 399
7.1 IMAGE AND NULLSPACE PROJECTORS 400
IMAGE 4
XII C O N T E N T S
7.2 MATTERS OF A PROPERLY STATED LEADING TERM 402
7.3 THE BASIC STEP OF THE SEQUENCE 404
7.3.1 BASIS REPRESENTATION METHODS 406
7.3.2 BASIS REPRESENTATION METHODS-REGULAR CASE 408
7.3.3 PROJECTOR REPRESENTATION METHOD 409
7.4 MATRIX FUNCTION SEQUENCES 413
7.4.1 STEPPING LEVEL BY LEVEL 413
7.4.2 INVOLVED VERSION FOR THE REGULAR CASE 415
7.4.3 COMPUTING CHARACTERISTIC VALUES AND INDEX CHECK 416
8 ASPECTS OF THE NUMERICAL TREATMENT OF HIGHER INDEX DAES 419
8.1 PRACTICAL INDEX CALCULATION 419
8.2 CONSISTENT INITIALIZATION 424
8.3 NUMERICAL INTEGRATION 426
8.4 NOTES AND REFERENCES 437
PART IV ADVANCED TOPICS
9 QUASI-REGULAR DAES 44 1
9.1 QUASI-PROPER LEADING TERMS 441
9.2 QUASI-ADMISSIBLE MATRIX FUNCTION SEQUENCES AND ADMISSIBLE PROJECTOR
FUNCTIONS 446
9.3 QUASI-REGULARITY 452
9.4 LINEARIZATION 455
9.5 A DAE TRANSFERABLE INTO SCF IS QUASI-REGULAR 457
9.6 DECOUPLING OF QUASI-REGULAR LINEAR DAES 462
9.7 DIFFICULTIES ARISING WITH THE USE OF SUBNULLSPACES 468
9.8 NOTES AND REFERENCES 471
9.9 HIERARCHY O F QUASI-ADMISSIBLE PROJECTOR FUNCTION SEQUENCES FOR
GENERAL NONLINEAR DAES 475
10 NONREGULAR DAES 477
10.1 THE SCOPE O F INTERPRETATIONS 478
10.2 LINEAR DAES 482
10.2.1 TRACTABILITY INDEX 482
10.2.2 GENERAL DECOUPLING 486
10.2.2.1 HAS FULL COLUMN RANK 489
10.2.2.2 TRACTABILITY INDEX 1, G HAS A NONTRIVIAL NULLSPACE 493
10.2.2.3 TRACTABILITY INDEX 2, G2 HAS A NONTRIVIAL NULLSPACE 497
10.3 UNDERDETERMINED NONLINEAR DAES 499
10.4 NOTES AND REFERENCES 502
IMAGE 5
CONTENTS XIII
11 MINIMIZATION WITH CONSTRAINTS DESCRIBED BY DAES 505
11.1 ADJOINT AND SELF-ADJOINT DAES 505
11.2 EXTREMAL CONDITIONS AND THE OPTIMALITY DAE 510
11.2.1 A NECESSARY EXTREMAL CONDITION AND THE OPTIMALITY D A E . . . .
510 11.2.2 A PARTICULAR SUFFICIENT EXTREMAL CONDITION 520
11.3 SPECIFICATION FOR CONTROLLED DAES 522
11.4 LINEAR-QUADRATIC OPTIMAL CONTROL AND RICCATI FEEDBACK SOLUTION . .
. . 525 11.4.1 SUFFICIENT AND NECESSARY EXTREMAL CONDITIONS 526
11.4.2 RICCATI FEEDBACK SOLUTION 527
11.5 NOTES AND REFERENCES 536
12 ABSTRACT DIFFERENTIAL-ALGEBRAIC EQUATIONS 539
12.1 INDEX CONSIDERATIONS FOR ADAES 540
12.2 ADAE EXAMPLES 544
12.2.1 CLASSICAL PARTIAL DIFFERENTIAL EQUATIONS 545
12.2.1.1 WAVE EQUATION 545
12.2.1.2 HEAT EQUATION 546
12.2.2 A SEMI-EXPLICIT SYSTEM WITH PARABOLIC AND ELLIPTIC PARTS . . . .
548 12.2.3 A COUPLED SYSTEM OF A PDE AND FREDHOLM INTEGRAL EQUATIONS 552
12.2.4 A PDE AND A DAE COUPLED BY A RESTRICTION OPERATOR 554
12.3 LINEAR ADAES WITH MONOTONE OPERATORS 554
12.3.1 BASIC FUNCTIONS AND FUNCTION SPACES 555
12.3.2 GALERKIN APPROACH 558
12.3.3 SOLVABILITY 564
12.3.4 CONTINUOUS DEPENDENCE ON THE DATA 571
12.3.5 STRONG CONVERGENCE OF THE GALERKIN METHOD 574
12.4 NOTES AND REFERENCES 577
APPENDICES 581
A LINEAR ALGEBRA - BASICS 581
A.L PROJECTORS AND SUBSPACES 581
A.2 GENERALIZED INVERSES 589
A.3 PARAMETER-DEPENDENT MATRICES AND PROJECTORS 591
A.4 VARIABLE SUBSPACES 594
B TECHNICAL COMPUTATIONS 599
B.L PROOF O F LEMMA 2.12 599
B.2 PROOF O F LEMMA 2.41 605
B.3 ADMISSIBLE PROJECTORS FOR NX + X = R 612
C ANALYSIS 627
C. 1 A REPRESENTATION RESULT 627
IMAGE 6
X I V C O N T E N T S
C.2 ODES 629
C.3 BASICS FOR EVOLUTION EQUATIONS 632
REFERENCES 637
INDEX 647
|
| any_adam_object | 1 |
| author | Lamour, René März, Roswitha 1940- Tischendorf, Caren 1969- |
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| ctrlnum | (OCoLC)833397732 (DE-599)DNB1017779376 |
| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
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| id | DE-604.BV040929161 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:27:24Z |
| institution | BVB |
| isbn | 3642275540 9783642275548 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025908136 |
| oclc_num | 833397732 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-824 DE-355 DE-BY-UBR DE-11 DE-188 DE-83 |
| owner_facet | DE-19 DE-BY-UBM DE-824 DE-355 DE-BY-UBR DE-11 DE-188 DE-83 |
| physical | XXVII, 649 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series2 | Differential-algebraic equations forum, DAE-F |
| spellingShingle | Lamour, René März, Roswitha 1940- Tischendorf, Caren 1969- Differential-algebraic equations a projector based analysis Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd |
| subject_GND | (DE-588)4229517-8 |
| title | Differential-algebraic equations a projector based analysis |
| title_auth | Differential-algebraic equations a projector based analysis |
| title_exact_search | Differential-algebraic equations a projector based analysis |
| title_full | Differential-algebraic equations a projector based analysis René Lamour ; Roswitha März ; Caren Tischendorf |
| title_fullStr | Differential-algebraic equations a projector based analysis René Lamour ; Roswitha März ; Caren Tischendorf |
| title_full_unstemmed | Differential-algebraic equations a projector based analysis René Lamour ; Roswitha März ; Caren Tischendorf |
| title_short | Differential-algebraic equations |
| title_sort | differential algebraic equations a projector based analysis |
| title_sub | a projector based analysis |
| topic | Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd |
| topic_facet | Differential-algebraisches Gleichungssystem |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3931946&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025908136&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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