Differential models: an introduction with Mathcad
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
2005
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 232 S. |
| ISBN: | 3540208526 |
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| 245 | 1 | 0 | |a Differential models |b an introduction with Mathcad |c Alexander Solodov ; Valery Ochkov |
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Record in the Search Index
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| adam_text | ALEXANDER SOLODOV
VALERY OCHKOV
DIFFERENTIAL MODELS
AN INTRODUCTIO
N WITH MATHCAD
WITH 169 FIGURES
^Y SPRINGER
CONTENTS
DIFFERENTIAL MATHEMATICAL MODELS 1
1.1 INTRODUCTION 1
1.2 LAWS IN THE DIFFERENTIAL FORM 1
1.3 MODELS OF GROWTH 8
1.4 CONSERVATION LAWS 14
1.5 CONSERVATION LAW FOR TRAFFIC PROBLEM 23
1.6 ONE-DIMENSIONAL STATIONARY MODELS: FUEL ELEMENT 29
1.7 CONCLUSION 33
INTEGRABLE DIFFERENTIAL EQUATIONS 37
2.1 INTRODUCTION 37
2.2 FIRST-ORDER LINEAR EQUATIONS 37
2.3 LINEAR HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS 41
2.4 LINEAR INHOMOGENEOUS EQUATIONS 43
2.5 EQUATIONS WITH SEPARABLE VARIABLES 43
2.6 HOMOGENEOUS DIFFERENTIAL EQUATIONS 44
2.7 DEPRESSION OF EQUATION 44
2.8 CONCLUSION 46
DYNAMIC MODEL OF SYSTEMS WITH HEAT GENERATION 47
3.1 INTRODUCTION 47
3.2 MATHEMATICAL MODEL 47
3.3 PHASE-PLANE PORTRAIT. STABLE AND UNSTABLE EQUILIBRIUM 50
3.4 STATE SET REPRESENTATION 51
3.5 PLOTTING THE BIFURCATION SET 53
3.6 FOLD CATASTROPHE 54
3.7 CATASTROPHIC JUMPS AT SMOOTH VARIATION OF PARAMETERS 55
3.8 TIME EVOLUTION OF SYSTEM WITH HEAT GENERATION 57
3.9 CONCLUSION 60
STIFF DIFFERENTIAL EQUATIONS 61
4.1 INTRODUCTION 61
4.2 MODEL DIFFERENTIAL EQUATION 62
4.3 METHOD RKFIXED. NUMERICAL INSTABILITY 63
4.4 METHOD RKADAPT. INTEGRATION STEP PROBLEM 68
4.5 METHOD STIFFR. SOLUTION OF STIFF MODEL EQUATION 70
4.6 METHOD STIFFR. SOLUTION OF CHEMICAL KINETICS EQUATIONS 72
4.7 EXPLICIT AND IMPLICIT METHODS 74
4.8 JACOBIAN MATRIX 76
4.9 CONCLUSION 77
X CONTENTS
HEAT TRANSFER NEAR THE STAGNATION POINT AT CROSS TUBE FLOW 79
5.1 INTRODUCTION 79
5.2 THE INTEGRAL EQUATION OF A THERMAL BOUNDARY LAYER 80
5.3 MATHEMATICAL FORMULATION OF THE PROBLEM 82
5.4 EXTERNAL FLOW VELOCITY DISTRIBUTION 84
5.5 ANALYSIS FOR THE STAGNATION POINT 86
5.6 DIMENSIONLESS FORMULATION 89
5.7 OPTIMIZATION ALGORITHM FOR THE RIGHT-HAND SIDE 90
5.8 NUMERICAL INTEGRATION WITH THE BUILT-IN FUNCTION ODESOLVE 91
5.9 CONCLUSION 93
THE FALKNER-SKAN EQUATION OF BOUNDARY LAYER 95
6.1 INTRODUCTION 95
6.2 MODEL CONSTRUCTION 99
6.3 BOUNDARY-VALUE PROBLEM. METHOD SBVAL 101
6.4 THE SOLUTION OF THE INITIAL PROBLEM. METHOD RKFIXED 103
6.5 FLOW FIELD IMAGING 105
6.6 BOUNDARY LAYER ON PERMEABLE WALLS 107
6.7 THERMAL BOUNDARY LAYER. HEAT TRANSFER LAW 112
6.8 TROUBLES WITH ODESOLVE 119
6.9 CONCLUSION 120
RAYLEIGH S EQUATION: HYDRODYNAMICAL INSTABILITY 123
7.1 INTRODUCTION 123
7.2 HYDRODYNAMIC EQUATIONS FOR FREE SHEAR FLOW 124
7.3 PERTURBATION METHOD. LINEARIZATION 125
7.4 TRANSITION TO COMPLEX DOMAIN 127
7.5 NUMERICAL INTEGRATION IN THE COMPLEX DOMAIN: PROGRAM EULER 130
7.6 INTEGRATION AND SEARCH OF EIGENVALUES 131
7.7 RETURNING TO THE REAL DOMAIN 134
7.8 CONCLUSION 136
KINEMATIC WAVES OF CONCENTRATION IN ION-EXCHANGE FILTER 137
8.1 INTRODUCTION 137
8.2 CONSERVATION EQUATION FOR CONCENTRATION IN FILTER 138
8.3 WAVE EQUATION FOR CONCENTRATION 140
8.4 DIMENSIONLESS FORMULATION 141
8.5 ISOTHERM OF ADSORPTION 142
8.6 SOLVING A WAVE EQUATION USING METHOD OF CHARACTERISTICS 146
8.7 CONCLUSION 150
KINEMATIC SHOCK
WAVE
S
151
9.1 INTRODUCTION 151
9.2 CONSERVATION EQUATION IN FINITE-DIFFERENCE FORM 152
9.3 DISCONTINUOUS SOLUTIONS. SHOCK WAVES 154
9.4 MACCORMACK METHOD. COMPUTING PROGRAM MCCRM 156
CONTENTS XI
9.5 SHOCKWAVE
S OF CONCENTRATION IN A FILTER 158
9.6 SHOCK WAVES ON A MOTORWAY 165
9.7 GRAVITATIONAL BUBBLE FLOW. STEAM-CONTENT SHOCK WAVES 170
9.8 CONCLUSION 180
10 NUMERICAL MODELING OF THE CPU-BOARD TEMPERATURE FIELD 181
10.1 INTRODUCTION 181
10.2 BUILT-IN FUNCTIONS FOR PARTIAL DIFFERENTIAL EQUATIONS 183
10.3 FINITE-DIFFERENCE APPROXIMATION 184
10.4 ITERATION METHOD OF SOLUTION. PROGRAM PLATE 186
10.5 THERMAL MODEL OF THE CPU-BOARD 187
10.6 PROBLEM OF ORBITAL PLATFORM. FUNCTION BVALFIT 191
10.7 CONCLUSION 196
11
TEMPERATURE
WAVE
S 203
11.1 INTRODUCTION 203
11.2 FORMULATION OF THE BOUNDARY-VALUE PROBLEM 204
11.3 DISCRETIZATION 204
11.4 TDMA: COMPUTING PROGRAMS COEF AND SYSTRD 208
11.5 COMPUTATIONAL MODELING OF CYCLICAL THERMAL ACTION 211
11.6 BUILT-IN FUNCTION PDESOLVE 214
11.7 CONCLUSION 217
LITERATURE 219
APPENDIX: BUILT-IN SOLVERS FOR ODE 223
INDEX 231
|
| any_adam_object | 1 |
| author | Solodov, Aleksandr P. Ochkov, Valery |
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| author_role | aut aut |
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| dewey-hundreds | 600 - Technology (Applied sciences) |
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| dewey-tens | 620 - Engineering and allied operations |
| discipline | Maschinenbau / Maschinenwesen Mathematik |
| format | Book |
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| language | German |
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| spelling | Solodov, Aleksandr P. Verfasser aut Differential models an introduction with Mathcad Alexander Solodov ; Valery Ochkov Berlin [u.a.] Springer 2005 XI, 232 S. txt rdacontent n rdamedia nc rdacarrier MathCAD Ingenieurwissenschaften Mathematisches Modell Differential equations Engineering Mathematical models Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Technik (DE-588)4059205-4 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Technik (DE-588)4059205-4 s Mathematisches Modell (DE-588)4114528-8 s Differentialgleichung (DE-588)4012249-9 s DE-604 Ochkov, Valery Verfasser aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013005543&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Solodov, Aleksandr P. Ochkov, Valery Differential models an introduction with Mathcad MathCAD Ingenieurwissenschaften Mathematisches Modell Differential equations Engineering Mathematical models Differentialgleichung (DE-588)4012249-9 gnd Technik (DE-588)4059205-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4059205-4 (DE-588)4114528-8 |
| title | Differential models an introduction with Mathcad |
| title_auth | Differential models an introduction with Mathcad |
| title_exact_search | Differential models an introduction with Mathcad |
| title_full | Differential models an introduction with Mathcad Alexander Solodov ; Valery Ochkov |
| title_fullStr | Differential models an introduction with Mathcad Alexander Solodov ; Valery Ochkov |
| title_full_unstemmed | Differential models an introduction with Mathcad Alexander Solodov ; Valery Ochkov |
| title_short | Differential models |
| title_sort | differential models an introduction with mathcad |
| title_sub | an introduction with Mathcad |
| topic | MathCAD Ingenieurwissenschaften Mathematisches Modell Differential equations Engineering Mathematical models Differentialgleichung (DE-588)4012249-9 gnd Technik (DE-588)4059205-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | MathCAD Ingenieurwissenschaften Mathematisches Modell Differential equations Engineering Mathematical models Differentialgleichung Technik |
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