Differential and differential-algebraic systems for the chemical engineer: solving numerical problems
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2014
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVI, 286 S. Ill., graph. Darst. 244 mm x 170 mm |
| ISBN: | 9783527332755 9783527667109 |
Staff View
MARC
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Record in the Search Index
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| adam_text |
CONTENTS
PREFACE IX
1 DEFINITE INTEGRALS 1
1.1 INTRODUCTION 1
1.2 CALCULATION OF WEIGHTS 2
1.3 ACCURACY OF NUMERICAL METHODS 3
1.4 MODIFICATION OF THE INTEGRATION INTERVAL 4
1.5 MAIN INTEGRATION METHODS 5
1.5.1 NEWTON-COTES FORMULAE 5
1.5.2 GAUSS FORMULAE 6
1.6 ALGORITHMS DERIVED FROM THE TRAPEZOID METHOD 9
1.6.1 EXTENDED NEWTON-COTES FORMULAE 10
1.6.2 ERROR IN THE EXTENDED FORMULAE 11
1.6.3 EXTRAPOLATION OF THE EXTENDED FORMULAE 12
1.7 ERROR CONTROL 15
1.8 IMPROPER INTEGRALS 16
1.9 GAUSS-KRONROD ALGORITHMS 17
1.10 ADAPTIVE METHODS 19
1.10.1 METHOD DERIVED FROM THE GAUSS-KRONROD ALGORITHM 20
1.10.2 METHOD DERIVED FROM THE EXTENDED TRAPEZOID ALGORITHM 21
1.10.3 METHOD DERIVED FROM THE GAUSS-LOBATTO ALGORITHM 22
1.11 PARALLEL COMPUTATIONS 23
1.12 CLASSES FOR DEFINITE INTEGRALS 23
1.13 CASE STUDY: OPTIMAL ADIABATIC BED REACTORS FOR SULFUR DIOXIDE WITH
COLD SHOT COOLING 26
2 ORDINARY DIFFERENTIAL EQUATIONS SYSTEMS 31
2.1 INTRODUCTION 31
2.2 ALGORITHM ACCURACY 35
2.3 EQUATION AND SYSTEM CONDITIONING 36
2.4 ALGORITHM STABILITY 40
2.5 STIFF SYSTEMS 48
HTTP://D-NB.INFO/1050181050
VI J CONTENTS
2.6 MULTISTEP AND MULTIVALUE ALGORITHMS FOR STIFF SYSTEMS 50
2.7 CONTROL OF THE INTEGRATION STEP 51
2.8 RUNGE-KUTTA METHODS 53
2.9 EXPLICIT RUNGE-KUTTA METHODS 54
2.9.1 STRATEGY TO AUTOMATICALLY CONTROL THE INTEGRATION STEP 56
2.9.2 ESTIMATION OF THE LOCAL ERROR 58
2.9.2.1 RUNGE-KUTTA-MERSON ALGORITHM 58
2.9.2.2 RICHARDSON EXTRAPOLATION 59
2.9.2.3 EMBEDDED ALGORITHMS 59
2.10 CLASSES BASED ON RUNGE-KUTTA ALGORITHMS IN THE
BZZMATH LIBRARY 61
2.11 SEMI-IMPLICIT RUNGE-KUTTA METHODS 64
2.12 IMPLICIT AND DIAGONALLY IMPLICIT RUNGE-KUTTA METHODS 66
2.13 MULTISTEP ALGORITHMS
68
2.13.1 ADAMS-BASHFORTH ALGORITHMS 70
2.13.2 ADAMS-MOULTON ALGORITHMS 71
2.14 MULTIVALUE ALGORITHMS 72
2.14.1 CONTROL OF THE LOCAL ERROR 76
2.14.2 CHANGE THE INTEGRATION STEP 78
2.14.3 CHANGING THE METHOD ORDER 79
2.14.4 STRATEGY FOR STEP AND ORDER SELECTION 82
2.14.5 INITIALIZING A MULTIVALUE METHOD 84
2.14.6 SELECTING THE FIRST INTEGRATION STEP 84
2.14.7 SELECTING THE MULTIVALUE ALGORITHMS 84
2.14.7.1 ADAMS-MOULTON ALGORITHMS 85
2.14.7.2 GEAR ALGORITHMS 85
2.14.8 NONLINEAR SYSTEM SOLUTION
86
2.15 MULTIVALUE ALGORITHMS FOR NONSTIFF PROBLEMS
88
2.16 MULTIVALUE ALGORITHMS FOR STIFF PROBLEMS 90
2.16.1 ROBUSTNESS IN STIFF PROBLEMS 93
2.16.1.1 EIGENVALUES WITH A VERY LARGE IMAGINARY PART 93
2.16.1.2 PROBLEMS WITH HARD DISCONTINUITIES 93
2.16.1.3 VARIABLE CONSTRAINTS 94
2.16.2 EFFICIENCY IN STIFF PROBLEMS 95
2.16.2.1 WHEN TO FACTORIZE THE MATRIX G 95
2.16.2.2 HOW TO FACTORIZE THE MATRIX G 96
2.16.2.3 WHEN TO UPDATE THE JACOBIAN J 96
2.16.2.4 HOW TO UPDATE THE JACOBIAN J 97
2.17 MULTIVALUE CLASSES IN BZZMATH LIBRARY 99
2.18 EXTRAPOLATION METHODS 107
2.19 SOME CAVEATS 108
3
3.1
3.2
ODE: CASE STUDIES 111
INTRODUCTION 111
NONSTIFF PROBLEMS 111
CONTENTS | VII
3.3 VOLTERRA SYSTEM 116
3.4 SIMULATION OF CATALYTIC EFFECTS 117
3.5 OZONE DECOMPOSITION 119
3.6 ROBERTSON'S KINETIC 120
3.7 BELOUSOV'S REACTION 121
3.8 FLUIDIZED BED 122
3.9 PROBLEM WITH DISCONTINUITIES 123
3.10 CONSTRAINED PROBLEM 124
3.11 HIRES PROBLEM 126
3.12 VAN DER POL OSCILLATOR 128
3.13 REGRESSION PROBLEMS WITH AN ODE MODEL 129
3.14 ZERO-CROSSING PROBLEM 139
3.15 OPTIMIZATION-CROSSING PROBLEM 142
3.15.1 OPTIMIZATION OF A BATCH REACTOR 142
3.15.2 MAXIMUM LEVEL IN A GRAVITY-FLOW TANK IN TRANSIENT
CONDITIONS 145
3.15.3 OPTIMIZATION OF A BATCH REACTOR 148
3.16 SPARSE SYSTEMS 150
3.17 USE OF ODE SYSTEMS TO FIND STEADY-STATE CONDITIONS OF CHEMICAL
PROCESSES 155
3.18 INDUSTRIAL CASE: SPECTROKINETIC MODELING 157
3.18.1 CATALYTIC-POST-PROCESSOR J59
3.18.2 NONREACTIVE CFD MODELING 159
3.18.3 USER-DEFINED FUNCTION 160
3.18.4 REACTOR MODELING 160
3.18.5 NUMERICAL METHODS 162
3.18.6 DYNAMIC SIMULATION OF AN OPERANDO FTIR CELL USED TO STUDY NOX
STORAGE ON A LNT CATALYST 163
3.18.7 CAT-PP SIMULATION RESULTS 166
3.18.8 NOMENCLATURE 169
4 DIFFERENTIAL AND ALGEBRAIC EQUATION SYSTEMS 171
4.1 INTRODUCTION 171
4.2 MULTIVALUE METHOD 174
4.3 DAE CLASSES IN THE BZZMATH LIBRARY 175
5 DAE: CASE STUDIES 187
5.1 INTRODUCTION 187
5.2 VAN DER POL OSCILLATOR 187
5.3 REGRESSION PROBLEMS WITH THE DAE MODEL 189
5.4 SPARSE STRUCTURED MATRICES 193
5.5 INDUSTRIAL CASE: DISTILLATION UNIT 199
5.5.1 MANAGEMENT OF SYSTEM SPARSITY AND UNSTRUCTURED
ELEMENTS 200
5.5.2 DAE SOLVER FOR PARTIALLY STRUCTURED SYSTEMS 201
VIII
| CONTENTS
5.5.3 CASE-STUDY FOR SOLVER VALIDATION: NONEQUILIBRIUM DISTILLATION
COLUMN MODEL 202
5.5.4 NUMERICAL RESULTS 205
NOTATIONS FOR TABLE 5.1 208
SUBSCRIPTS 208
SYMBOLS 208
6 BOUNDARY VALUE PROBLEMS 209
6.1 INTRODUCTION 209
6.1.1 INTEGRAL RELATIONSHIPS 211
6.1.2 CONTINUATION METHODS 212
6.1.3 PROBLEMS WITH AN UNKNOWN CONSTANT PARAMETER 214
6.1.4 PROBLEM WITH UNKNOWN BOUNDARY 214
6.2 SHOOTING METHODS 215
6.3 SPECIAL BOUNDARY VALUE PROBLEMS 217
6.3.1 RUNGE-KUTTA IMPLICIT METHODS 218
6.4 MORE GENERAL BVP METHODS 221
6.4.1 COLLOCATION METHOD 222
6.4.2 GALERKIN METHOD 222
6.4.3 MOMENTUM METHOD 223
6.4.4 LEAST-SQUARES METHOD 223
6.5 SELECTION OF THE APPROXIMATING FUNCTION 224
6.6 WHICH AND HOW MANY SUPPORT POINTS HAVE TO BE CONSIDERED? 225
6.7 WHICH VARIABLES SHOULD BE SELECTED AS ADAPTIVE PARAMETERS? 231
6.8 THE BVP SOLUTION CLASSES IN THE BZZMATH LIBRARY 237
6.9 ADAPTIVE MESH SELECTION 251
6.10 CASE STUDIES 253
REFERENCE 265
APPENDIX A: LINKING THE BZZMATH LIBRARY TO MATLAB 269
A.L INTRODUCTION 269
A.2 BZZSUM FUNCTION 269
A.2.1 HEADER FILE 270
A.2.2 MEX FUNCTION 270
A.2.3 C++ PART 271
A.2.4 COMPILING 272
A.3 CHEMICAL ENGINEERING EXAMPLE 272
A.3.1 DEFINITION OF A NEW CLASS 274
A.3.2 MAIN PROGRAM IN C++ 275
A.3.3 MAIN PROGRAM IN MATLAB 277
APPENDIX B: COPYRIGHTS 279
INDEX 281 |
| any_adam_object | 1 |
| author | Buzzi-Ferraris, Guido Manenti, Flavio |
| author_GND | (DE-588)140951458 (DE-588)140951474 |
| author_facet | Buzzi-Ferraris, Guido Manenti, Flavio |
| author_role | aut aut |
| author_sort | Buzzi-Ferraris, Guido |
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| building | Verbundindex |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3502466 |
| dewey-search | 515.3502466 |
| dewey-sort | 3515.3502466 |
| dewey-tens | 510 - Mathematics |
| discipline | Chemie / Pharmazie Mathematik |
| format | Book |
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| id | DE-604.BV042211181 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T01:58:55Z |
| institution | BVB |
| isbn | 9783527332755 9783527667109 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027649870 |
| oclc_num | 878979246 |
| open_access_boolean | |
| owner | DE-11 DE-92 |
| owner_facet | DE-11 DE-92 |
| physical | XVI, 286 S. Ill., graph. Darst. 244 mm x 170 mm |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Wiley-VCH |
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| spelling | Buzzi-Ferraris, Guido Verfasser (DE-588)140951458 aut Differential and differential-algebraic systems for the chemical engineer solving numerical problems Guido Buzzi-Ferraris ; Flavio Manenti Weinheim Wiley-VCH 2014 XVI, 286 S. Ill., graph. Darst. 244 mm x 170 mm txt rdacontent n rdamedia nc rdacarrier Differentialgleichungssystem (DE-588)4121137-6 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Technische Chemie (DE-588)4078178-1 gnd rswk-swf Chemische Verfahrenstechnik (DE-588)4069941-9 gnd rswk-swf Differentialgleichungssystem (DE-588)4121137-6 s Chemische Verfahrenstechnik (DE-588)4069941-9 s DE-604 Technische Chemie (DE-588)4078178-1 s Analysis (DE-588)4001865-9 s 1\p DE-604 Manenti, Flavio Verfasser (DE-588)140951474 aut Erscheint auch als Online-Ausgabe, EPUB 978-3-527-66712-3 Erscheint auch als Online-Ausgabe, MOBI 978-3-527-66711-6 Erscheint auch als Online-Ausgabe, PDF 978-3-527-66713-0 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4642564&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027649870&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Buzzi-Ferraris, Guido Manenti, Flavio Differential and differential-algebraic systems for the chemical engineer solving numerical problems Differentialgleichungssystem (DE-588)4121137-6 gnd Analysis (DE-588)4001865-9 gnd Technische Chemie (DE-588)4078178-1 gnd Chemische Verfahrenstechnik (DE-588)4069941-9 gnd |
| subject_GND | (DE-588)4121137-6 (DE-588)4001865-9 (DE-588)4078178-1 (DE-588)4069941-9 |
| title | Differential and differential-algebraic systems for the chemical engineer solving numerical problems |
| title_auth | Differential and differential-algebraic systems for the chemical engineer solving numerical problems |
| title_exact_search | Differential and differential-algebraic systems for the chemical engineer solving numerical problems |
| title_full | Differential and differential-algebraic systems for the chemical engineer solving numerical problems Guido Buzzi-Ferraris ; Flavio Manenti |
| title_fullStr | Differential and differential-algebraic systems for the chemical engineer solving numerical problems Guido Buzzi-Ferraris ; Flavio Manenti |
| title_full_unstemmed | Differential and differential-algebraic systems for the chemical engineer solving numerical problems Guido Buzzi-Ferraris ; Flavio Manenti |
| title_short | Differential and differential-algebraic systems for the chemical engineer |
| title_sort | differential and differential algebraic systems for the chemical engineer solving numerical problems |
| title_sub | solving numerical problems |
| topic | Differentialgleichungssystem (DE-588)4121137-6 gnd Analysis (DE-588)4001865-9 gnd Technische Chemie (DE-588)4078178-1 gnd Chemische Verfahrenstechnik (DE-588)4069941-9 gnd |
| topic_facet | Differentialgleichungssystem Analysis Technische Chemie Chemische Verfahrenstechnik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4642564&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=027649870&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT buzziferrarisguido differentialanddifferentialalgebraicsystemsforthechemicalengineersolvingnumericalproblems AT manentiflavio differentialanddifferentialalgebraicsystemsforthechemicalengineersolvingnumericalproblems |