Control of Distributed Parameter Systems (eBook)

Proceedings of the Second IFAC Symposium, Coventry, Great Britain, 28 June - 1 July 1977

S. P. Banks, A. J. Pritchard (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
554 Seiten
Elsevier Science (Verlag)
9781483151120 (ISBN)

Infos

Control of Distributed Parameter Systems covers the proceedings of the Second IFAC Symposium, Coventry, held in Great Britain from June 28 to July 1, 1977. The book focuses on the methodologies, processes, and techniques in the control of distributed parameter systems, including boundary value control, digital transfer matrix, and differential equations. The selection first discusses the asymptotic methods in the optimal control of distributed systems; applications of distributed parameter control theory of a survey; and dual variational inequalities for external eigenvalue problems. The book also ponders on stochastic differential equations in Hilbert space and their application to delay systems and linear quadratic optimal control problem over an infinite time horizon for a class of distributed parameter systems. The manuscript investigates the semigroup approach to boundary value control and stability of nonlinear distributed parameter systems. Topics include boundary control action implemented through a dynamical system; classical boundary value controls; stability of nonlinear systems; and feedback control on the boundary. The text also focuses on the functional analysis interpretation of Lyapunov stability; method of multipliers for a class distributed parameter systems; and digital transfer matrix approach to distributed system simulation. The selection is a dependable source of data for readers interested in the control of distributed parameter systems.

Inhalt

Front Cover 1
Control of Distributed Parameter Systems 4
Copyrigh Page 5
Table of Contents 8
Foreword 12
CHAPTER 1. ASYMPTOTIC METHODS IN THE OPTIMAL CONTROL OF DISTRIBUTED SYSTEMS 14
1. INTRODUCTION 14
2. PERTURBATION OF THE STATE EQUATION. THE CASE OF A "CONTINUOUS" COST FUNCTION 16
3. PERTURBATION OF THE STATE EQUATION. THE CASE WHERE THE COST FUNCTION IS NOT DEFINED ON THE LIMIT SPACE. 20
4. PERTURBATION OF THE COST FUNCTION 26
5. DEGENERACY OF THE COST FUNCTION (CHEAP CONTROL) 28
6. PERTURBATIONS OF THE DOMAIN. 29
REFERENCES 33
CHAPTER 2. SOME RECENT APPLICATIONS OF DISTRIBUTED PARAMETER CONTROL THEORY A SURVEY 34
ABSTRACT 34
INTRODUCTION 34
BRIEF SUMMARY OF APPLIED DISTRIBUTED PARAMETER CONTROL THEORY 34
SOME REPORTED APPLICATIONS 35
CONCLUDING REMARKS 37
REFERENCES 37
CHAPTER 3. DUAL VARIATIONAL INEQUALITIES FOR EXTREMAL EIGENVALUE PROBLEMS 48
ABSTRACT 48
INTRODUCTION 48
2. STABILITY PROBLEMS FOR PERIODIC DIFFERENTIAL EQUATIONS 49
3. STRUCTURAL OPTIMIZATION PROBLEMS 51
4. NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS 52
5. DUAL EXTREMAL EIGENVALUE PROBLEMS 53
References 57
CHAPTER 4. STOCHASTIC DIFFERENTIAL EQUATIONS IN HILBERT SPACE AND THEIR APPLICATION TO DELAY SYSTEMS 58
ABSTRACT 58
INTRODUCTION 58
2. PRELIMINARIES 59
3. STOCHASTIC EVOLUTION EQUATIONS WITH STATE DEPENDENT NOISE 60
4. STOCHASTIC LINEAR DELAY EQUATIONS WITH MARTINGALE NOISE 64
REFERENCES 67
CHAPTER 5. THE LINEAR QUADRATIC OPTIMAL CONTROL PROBLEM OVER AN INFINITE TIME HORIZON FOR A CLASS OF DISTRIBUTED PARAMETER SYSTEMS 70
ABSTRACT 70
1. INTRODUCTION 70
2. PRELIMINARIES AND PROBLEM FORMULATION 71
3. ASYMPTOTIC BEHAVIOUR AND L2-STABILITY 71
4. THE OPTIMAL CONTROL PROBLEM IN [0,-[ 72
5. RELATIONSHIPS BETWEEN CONTROLLABILITY AND STABILIZABILITY 73
6. EXAMPLES 75
REFERENCES 76
CHAPTER 6. INITIAL-VALUE CONTROL OF THE KORTEWEG-DE VRIES EQUATION 80
ABSTRACT 80
INTRODUCTION 80
WELL-POSEDNESS OF THE INITIAL-VALUE PROBLEM 80
AN INITIAL-VALUE CONTROL PROBLEM 81
REFERENCES 84
CHAPTER 7. ON QUASIEQUILIBRIUM STATES AND RANGE DEGENERACY FOR LINEAR SEMIGROUP SYSTEMS 88
ABSTRACT 88
INTRODUCTION 88
BASIC DEFINITIONS 88
FUNDAMENTAL PROPERTIES OF QEQ AND DED 89
DUALITY BETWEEN QEQ AND DED 92
MORE ON FDE SYSTEMS 92
APPLICATION TO STABILIZATION PROBLEM 93
CONCLUDING REMARKS 96
ACKNOWLEDGEMENT 96
REFERENCES 96
CHAPTER 8. TIME-INVARIANCE OF THE REACHABLE SET FOR LINEAR CONTROL PROBLEMS 98
References 102
CHAPTER 9. SEMIGROUPS ON PRODUCT SPACES WITH APPLICATION TO INITIAL VALUE PROBLEMS WITH NON-LOCAL BOUNDARY CONDITIONS 104
ABSTRACT 104
1. INTRODUCTION 104
2. STATEMENT OF RESULTS 105
3. SOME SPECIAL CASES 106
4. PROOF OF THEOREM 2.1 (OUTLINE) 106
5. APPLICATIONS 108
REFERENCES 111
CHAPTER 10. A SEMIGROUP APPROACH TO BOUNDARY VALUE CONTROL 112
1. INTRODUCTION 112
2. BOUNDARY CONTROL ACTION IMPLEMENTED THROUGH A DYNAMICAL SYSTEM. Examples 112
3. BOUNDARY CONTROL ACTION IMPLEMENTED THROUGH A DYNAMICAL SYSTEM , General model 113
4. DISCUSSION OF THE MODEL 116
5. FEEDBACK CONTROL ON THE BOUNDARY 117
6. SOME OPEN PROBLEMS 118
7. CLASSICAL BOUNDARY VALUE CONTROLS 118
REFERENCES 120
CHAPTER 11. STABILITY OF NONLINEAR DISTRIBUTED PARAMETER SYSTEMS 122
ABSTRACT 122
1. INTRODUCTION 122
2. SURVEY OF THE LITERATURE 122
3. EXISTENCE ..T UNIQUENESS OF SOLUTIONS 123
4. STABILITY OF LINEAR SYSTEMS 124
5. NONLINEAR SYSTEMS 126
6. FINAL REMARKS 131
7. REFERENCES 131
CHAPTER 12. STABILITY OF ABSTRACT EVOLUTION EQUATIONS 134
1 INTRODUCTION 134
2 PERTURBATIONS OF LINEAR SEMI-GROUPS 135
3 PERTURBATION THEOREMS FOR NON-LINEAR OPERATORS 141
References 145
CHAPTER 13. BIFURCATIONS TO DIVERGENCE AND FLUTTER IN FLOW-INDUCED OSCILLATIONS:an infinite dimensional analysis 146
ABSTRACT 146
1. INTRODUCTION 146
2. EXISTENCE, UNIQUENESS AND SMOOTHNESS 146
3. CENTRE MANIFOLD THEORY AND BIFURCATIONS 148
4. FINITE DIMENSIONAL APPROXIMATIONS AND CONVERGENCE 150
5. AN EXAMPLE BASED ON A TWO MODE MODEL OF PANEL FLUTTER 151
6. CONCLUSIONS 152
ACKNOWLEDGEMENTS 153
REFERENCES 153
CHAPTER 14. ON THE PATH INTEGRAL AND LYAPUNOV FUNCTIONAL FOR A CLASS OF DISTRIBUTED SYSTEMS 160
ABSTRACT 160
1. INTRODUCTION 160
2. STATEMENT OF PROBLEMS AND PATH INTEGRALS 160
3. RESULTS AND LYAPUNOV FUNCTIONALS 162
4. APPLICATIONS 164
5. CONCLUSIONS 167
Acknowledgment 167
APPENDIX A 167
APPENDIX B 167
References 169
CHAPTER 15. THE FUNCTIONAL ANALYSIS INTERPRETATION OF LYAPUNOV STABILITY 170
ABSTRACT 170
INTRODUCTION 170
DYNAMIC SYSTEM 170
DEFINITIONS OF STABILITY 171
GENERAL IDEA OF THE LYAPUNOV METHOD 172
INTERPRETATION OF CLASSICAL METHODS 173
VECTOR LYAPUNOV PUNCTIONALS 174
CONCLUSIONS 174
REFERENCES 175
CHAPTER 16. STABILITY CONDITIONS AND DESIGN OF CONTROL USING LIAPUNOV-ZUBOV FUNCTIONALS 176
ABSTRACT 176
INTRODUCTION 176
THEOREMS ON THE STABILITY 177
INTEGRAL FORM OF THE LIAPUNOW-ZUBOV FUUCT10NALS 182
CONTROL OF PIPE LINES 182
REFERENCES 184
CHAPTER 17. ON THE METHOD OF MULTIPLIERS FOR A CLASS OF DISTRIBUTED PARAMETER SYSTEMS 186
ABSTRACT 186
1. INTRODUCTION 186
2. NOTATIONS AND ASSUMPTIONS 186
3. BOUNDARY CONTROL PROBLEMS 187
4. DISTRIBUTED CONTROL PROBLEMS 190
5. CONCLUDING REMARKS 193
REFERENCES 193
CHAPTER 18. A DIGITAL TRANSFER MATRIX APPROACH TO DISTRIBUTED SYSTEM SIMULATION 194
ABSTRACT 194
INTRODUCTION 194
DERIVATION OF THE ALGORITHMS 195
AN EXAMPLE: HEAT TRANSFER IN MULTI-LAYER SLABS 201
CONCLUSION 204
ACKNOWLEDGEMENTS 204
REFERENCES 204
CHAPTER 19. ERRORS IN THE FINITE DIFFERENCE SOLUTION OF HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS 206
INTRODUCTION 206
SYSTEM EQUATIONS 206
SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS 207
ERROR ANALYSIS 207
FINITE DIFFERENCE GRID SPACING 208
METHOD OF CHARACTERISTICS 209
EXAMPLE 209
CONCLUSION 210
REFERENCES 211
APPENDIX I 211
APPENDIX 2 211
CHAPTER 20. DESIGN OF DISTRIBUTED-PARAMETER OPTIMALCONTROLLERS AND FILTERS VIA WALSH-GALERKIN EXPANSIONS 214
ABSTRACT 214
INTRODUCTION 214
2. THE BASIC WALSH-GALERKIN EXPANSION TECHNIQUE 215
3. THE DISTRIBUTED-PARAMETER OPTIMAL CONTROLLER AND FILTER DESIGN PROBLEMS 218
4. WALSH-GALERKIN IMPLEMENTATION OF THE OPTIMAL CONTROLLER 220
5. IMPROVED WALSH-RITZ-GALERKIN EXPANSION TECHNIQUE 222
6. WALSH-GALERKIN SOLUTION OF DISTRIBUTED-PARAMETER VARIATIONAL PROBLEMS 223
7. EXAMPLES 226
8. CONCLUSION 227
REFERENCES 227
CHAPTER 21. OBSERVERS FOR BILINEAR DISTRIBUTED PARAMETER PROCESSES 232
ABSTRACT 232
1. INTRODUCTION 232
2. BILINEAR DISTRIBUTED PARAMETER SYSTEM - HEAT EXCHANGE PROCESS 233
3. BILINEAR OBSERVERS 235
4. LUMPED PARAMETER APPROXIMATION BY USING THE METHOD OF WEIGHTED RESIDUALS (MWR) 237
5. EXPERIMENTAL INVESTIGATION 238
6. CONCLUSION 241
REFERENCES 241
CHAPTER 22. INITIAL STATE DETERMINATION FOR DISTRIBUTED PARAMETER SYSTEMS WITH DISCRETE-TIME MEASUREMENT DATA 244
ABSTRACT 244
INTRODUCTION 244
STATEMENT OF THE PROBLEM 244
N-STEP OBSERVABILITY AND N-STEP OUTPUT CONTROLLABILITY WITH RESPECT TO THE INITIAL STATE 245
MINIMIZATION OF J(n) 246
DUAL PROBLEM 246
A WELL-POSED APPROXIMATION METHOD 246
THE SYSTEM WITH POINTWISE OBSERVATION 248
CONCLUSIONS 249
NUMERICAL RESULTS 249
REFERENCES 249
CHAPTER 23. PARAMETER AND STATE ESTIMATION FOR A DIFFUSION PROCESS 252
REFERENCES 258
CHAPTER 24. DIFFERENTIAL STATE SPACE DESCRIPTIONS OF NONLINEAR TIME VARIANT HEREDITARY DIFFERENTIAL SYSTEMS 260
ABSTRACT 260
.. INTRODUCTION 260
2. THE PROBLEM OF DIFFERENTIAL STATE SPACE DESCRIPTION 261
3. DIFFERENTIABILITY OF THE SEGMENT FUNCTION t —> xt
4. SOLUTIONS OF z(t) = A z(t) 268
5. CONCLUSIONS 270
REFERENCES 272
CHAPTER 25. F- REDUCTION OF THE OPERATOR RICCATI EQUATIONS FOR HEREDITARY DIFFERENTIAL SYSTEMS 274
1. INTRODUCTION 274
2. LINEAR AUTONOMOUS HDS 275
3. THE LINEAR QUADRATIC OPTIMAL CONTROL PROBLEM 277
REFERENCES 282
CHAPTER 26. OPTIMAL OUTPUT-FEEDBACK CONTROLLERS FOR LINEAR TIME-DELAY SYSTEMS 286
ABSTRACT 286
INTRODUCTION 286
PROBLEM FORMULATION 287
MAIN RESULT 288
CONCLUSION 289
REFERENCES 290
CHAPTER 28. FINITE DIFFERENCE APPROXIMATION OF STATE AND CONTROL CONSTRAINED OPTIMAL CONTROL PROBLEM FOR SYSTEM WITH DELAY 292
ABSTRACT 292
NOTATIONS 292
CONTINUOUS OPTIMAL CONTROL PROBLEM STATEMENT 292
LAGRANGE FORMALISM 293
DISCRETE OPTIMAL CONTROL PROBLEM STATEMENT 294
ESTIMATION OF THE RATE OF CONVERGENCE 296
REFERENCES 297
CHAPTER 29. NECESSARY AND SUFFICIENT CONDITIONS FOR DESIGNING OPTIMAL FEEDBACK CONTROLLERS FOR LINEAR DYNAMICAL SYSTEMS WITH MULTIPLE TIME DELAYS 298
ABSTRACT 298
I. INTRODUCTION 298
II. CANONICAL DECOMPOSITION 299
III. THE LINEAR-QUADRATIC REGULATOR THEORY FOR NON-DELAYED SYSTEMS 301
IV. THE LINEAR-QUADRATIC REGULATOR THEORY FOR DELAYED SYSTEMS 301
V. EXAMPLE 303
IV, CONCLUSION 303
ACKNOWLEDGMENTS 303
REFERENCES 303
CHAPTER 30. ON GOODNESS-OF-FIT STRUCTURE OF SOME DETERMINISTIC AND STOCHASTIC MODELS FOR EXPANDING ECONOMIES 306
ABSTRACT 306
1. INTRODUCTION 306
2. THE VON NEUMANN MODELS AND THEIR GENERALIZATIONS 307
3. TESTING STATISTICAL STRUCTURAL VALIDITY OF STOCHASTIC ECONOMIC MODELS 312
ACKNOWLEDGEMENT 319
REFERENCES 319
CHAPTER 31. ADAPTIVE OPEN LOOP CONTROL FOR A CLASS OF DISTRIBUTED PARAMETER SYSTEMS 322
ABSTRACT 322
SITUATION OF THE PROBLEM 322
METHODS OF SOLUTION 323
FORMULATION OF THE SOLUTION 324
SIMULATION - EXAMPLE 326
RESULTS 328
REFERENCES 330
CHAPTER 32. ON THE DISCRETE-TIME QUADRATIC OPTIMUM CONTROL PROBLEM IN REFLEXIVE BANACH SPACE 332
ABSTRACT 332
1. INTRODUCTION 332
2. NOTATION AND PRELIMINARIES 333
3. PROBLEM FORMULATION AND BASIC SOLUTION 334
4. THE OPTIMUM CONTROL LAW 335
5. OPTIMUM CONTROL PROBLEM ON INFINITE TIME SET 336
6. THE CONVERGENCE PROBLEM 337
CONCLUSIONS 340
ACKNOWLEDGEMENT 340
REFERENCES 340
CHAPTER 33. SIMPLIFIED OPTIMUM CONTROL OF DISTRIBUTED PARAMETER SYSTEMS 342
ABSTRACT 342
INTRODUCTION 342
OPEN-LOOP OPTIMAL CONTROL 343
CLOSED-LOOP CONTROL 343
NUMERICAL EXAMPLE 345
CONCLUSIONS 348
REFERENCES 348
CHAPTER 34. A STOCHASTIC DIFFERENTIAL GAME AS CONTROL PROBLEM WITH INFINITE DIMENSIONAL STATE SPACE 350
ABSTRACT 350
1 INTRODUCTION 350
2 GAUSS MEASURE AND WHITE NOISE 351
3 LINEAR-QUADRATIC GAME: LUMPED PARAMETER CASE 352
4 LINEAR-QUADRATIC GAME: DISTRIBUTED PARAMETER CASE 356
5 CONCLUSION 358
CHAPTER 35. FILTERING AND CONTROL OF DISTRIBUTED PARAMETER SYSTEMS WITH POINT OBSERVATIONS AND INPUTS 360
ABSTRACT 360
INTRODUCTION 360
1. THE MODEL AND OPTIMAL LOCATION PROBLEM 361
2. AN EXAMPLE OF A HEAT EQUATION 363
3. NUMERICAL RESULTS 364
4. CONCLUSION 367
REFERENCES 367
CHAPTER 36. THE SOLUTION OF SOME IDENTIFICATION PROBLEMS OF BIOMEDICAL SYSTEMS 372
ABSTRACT 372
INTRODUCTION 372
THE KINDS OF PROBLEMS 373
MATHEMATICAL FORMULATION OF THE PROBLEM 373
DESCRIPTION OF THE METHOD 374
ITERATIVE PROCESS 376
ERRORS 376
CONCLUSION 378
KEEERENOE 378
CHAPTER 37. GEOSTATISTICAL TECHNIQUES IN DISTRIBUTED PARAMETER SYSTEM ESTIMATION PROBLEMS 380
1 - INTRODUCTION 380
2 - GEOSTATISTICAL MODELS 381
3 - APPLICATION OF THE MODEL TO THE ESTIMATION OF A LINEAR FUNCTION OF A ReV 385
4 - USING I.R.F.k TO ESTIMATE LINEAR FUNCTIONS OF A NON STATIONARY RF 387
CONCLUSION 390
ACKNOWLEDGEMENTS 390
REFERENCES 390
CHAPTER 38. IDENTIFIABILITY OF INTERNAL AND BOUNDARY PARAMETERS IN SYSTEMS OF PARABOLIC TYPE 394
ABSTRACT 394
1. Introduction 394
2 . Statement of the Identiflability Problem 395
3 . Distributed Measurement 396
4 . Pointwise Measurement 401
5. Conclusion 404
Acknowledgement 404
REFERENCES 405
CHAPTER 39. FREQUENCY DOMAIN SIMULATION AND IDENTIFICATION OF DISTRIBUTED SYSTEMS 406
ABSTRACT 406
INTRODUCTION 406
THEORY 407
EXAMPLE 409
REFERENCES 412
CHAPTER 40. AN ATTEMPT TO IDENTIFY THE VISUAL AND MANUAL PHENOMENA FOR A HUMAN OPERATOR SUBMITTED TO VESTIBULAR STIMULATIONS (PITCH MOTION) DURINGVISUAL DETECTION TASKS 414
INTRODUCTION 414
I - STATEMENT OF THE PROBLEM 414
II - EXPERIMENTAL CONTROL SLT UP AND CHARACTERIZATION OF INPUT, OUTPUT AND PERTURBATION VARIABLES 415
Ill - PREVIOUS RESULTS (5.6) 416
IV- VISUAL TASK PARAMETERS IDENTIFICATION 418
V - SYNTHESIS OF THE RESULT. MODEL FOR THE HUMAN OPERATOR BEHAVIOR IN A MOVING MECHANICAL WORKING STATION 423
CONCLUSION 425
BIBLIOGRAPHY 425
CHAPTER 41. OPTIMAL CONTROL OF CHEMICAL PLANTS WITH STAGES SUBJECT TO RANDOM BREAKDOWNS 426
ABSTRACT 426
INTRODUCTION 426
MARKOV JUMP DISTURBANCES AND MARKOV DECISION PROCESSES 426
A BALANCING PROBLEM IN THE PRODUCTION OF VINYL CHLORIDE 428
A MARKOV CHAIN APPROXIMATION 430
DISCUSSION 433
REFERENCES 434
APPENDIX 434
CHAPTER 42. MWR APPROXIMATION AND MODAL CONTROL OF PARALLEL- AND COUNTER-FLOW HEAT EXCHANGERS 436
ABSTRACT 436
1. INTRODUCTION 436
2. MWR APPROXIMATE SYSTEMS 437
3. MODAL CONTROL OF THE HEAT EXCHANGERS 441
4. CONCLUSIONS 447
NOMENCLATURE 447
REFERENCES 447
CHAPTER 43. CONTROL OF A DISTRIBUTED PARAMETER SYSTEM USING VECTOR PERFORMANCE INDEX 450
ABSTRACT 450
INTRODUCTION 450
THE STEAM GENERATOR SYSTEM 451
PARAMETER OPTIMIZATION VIA VECTOR PERFORMANCE INDEX 457
NUMERICAL RESULTS - SASM 458
NONLINEAR STEAM GENERATOR SYSTEM PERFORMANCE 460
DISCUSSION AND CONCLUSIONS 461
REFERENCES 461
ACKNOWLEDGEMENT 462
CHAPTER 44. THE REAL TIME APPLICATION OF DISTRIBUTED PARAMETER STATE ESTIMATION THEORY TO A TWO DIMENSIONAL HEATED INGOT 464
ABSTRACT 464
INTRODUCTION 464
THE EXPERIMENTAL PROCESS 464
THE STATE ESTIMATOR 471
EXPERIMENTAL RESULTS 475
CONCLUSIONS 478
ACKNOWLEDGEMENTS 478
NOMENCLATURE 478
REFERENCES 479
CHAPTER 45. STABILITY OF COUNTERCURRENTLY COOLED FIXED BED REACTORS 482
ABSTRACT 482
INTRODUCTION 482
MOBEL CONSIDERATIONS 482
CONCLUSIONS 488
NOTATION 488
REFERENCES 489
CHAPTER 46. A REDUCED MODEL FOR OPTIMAL CONTROL OF A GAS DISTRIBUTION NETWORK 492
ABSTRACT 492
INTRODUCTION 492
THE FLOW CONTROL PROBLEM 492
FORMULATION OF MODEL 493
FORMULATION OF MODEL 493
MODEL REDUCTION 494
EVALUATION OF REDUCED MODELS 496
SYNTHESIS OF AN OPTIMAL CONTROL ALGORITHM 497
NOTATION 499
SUBSCRIPTS 500
BREAK LETTERS 500
REFERENCES 500
ACKNOWLEDGEMENT 500
CHAPTER 47. PHENOMENOLOGICAL INVESTIGATION OF A DISTRIBUTED PARAMETER MODEL FOR COORDINATING THE MECHANICAL ACTIVITY OF THE MAMMALIAN GUT 506
ABSTRACT 506
1. INTRODUCTION 506
2. MODELLING THEORY 507
3. SIMULATION RESULTS 516
4. CONCLUSIONS 521
5. ACKNOWLEDGEMENTS 521
6. REFERENCES 521
CHAPTER 48. OPTIMUM DESIGN OF DISTRIBUTED MASS AND STIFFNESS STRUCTURAL SYSTEMS UNDER CONSTRAINTS 524
ABSTRACT 524
INTRODUCTION 524
ANALYSIS 526
RESULTS 535
DISCUSSION 537
REFERENCES 538
CHAPTER 49. APPLICATIONS OF EXTENDED OPERATORS TO DIFFUSIVE SYSTEMS 540
ABSTRACT 540
1. INTRODUCTION 540
2. DERIVATION OF THE EXTENDED OPERATOR: AN EXAMPLE 541
3. EXTENDED OPERATOR TABLE FOR ID DIFFUSION EQUATION 541
5. HEAT DISTRIBUTION IN A COMPOSITE SLAB 542
6. FOURIER APPROXIMATIONS TO PERIOD 543
CONCLUSION 544
APPENDIX - DERIVATION OF THE EXTENDED OPERATOR 545
REFERENCES 545
LIST OF PARTICIPANTS 552
AUTHOR INDEX 554

Produkt-Details

• Erscheint lt. Verlag: 18.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Netzwerke
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• ISBN-13: 9781483151120 / 9781483151120