Mathematical modeling with multidisciplinary applications:
"This book details the interdisciplinary nature of mathematical modeling and numerical algorithms. It combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and in...
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| Format: | Book |
| Language: | English |
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Hoboken, NJ
Wiley
2013
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| Subjects: | |
| Online Access: | 80 Inhaltsverzeichnis |
| Summary: | "This book details the interdisciplinary nature of mathematical modeling and numerical algorithms. It combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Including case studies, worked examples, and exercises, it cover topics such as partial differential equations, fractional calculus, inverse problems by ODEs, semigroups, decision theory, risk analysis, Bayesian estimation, nonlinear PDEs in financial engineering, perturbation analysis, dynamic system modeling, and much more"-- |
| Item Description: | Literaturangaben |
| Physical Description: | XXXI, 557 S. Ill., graph. Darst. |
| ISBN: | 9781118294413 |
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| 245 | 1 | 0 | |a Mathematical modeling with multidisciplinary applications |c ed. by Xin-She Yang |
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Record in the Search Index
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|---|---|
| adam_text | Titel: Mathematical modeling with multidisciplinary applications
Autor: Yang, Xin-She
Jahr: 2013
CONTENTS
List of Figures xv
Preface xxiii
Acknowledgments xxvii
Editor and Contributors xxix
PART I INTRODUCTION AND FOUNDATIONS
1 Differential Equations 3
Xin-She Yang
1.1 Ordinary Differential Equations 4
1.1.1 First-Order ODEs 5
1.1.2 Higher-Order ODEs 6
1.1.3 Linear System 8
1.1.4 Sturm-Liouville Equation 8
1.2 Partial Differential Equations 10
1.2.1 First-Order PDEs 11
1.2.2 Classification of Second-Order PDEs 12
1.3 Classic Mathematical Models 12
1.4 Other Mathematical Models 14
1.5 Solution Techniques 15
1.5.1 Separation of Variables 15
1.5.2 Laplace Transform 18
1.5.3 Similarity Solution 19
1.5.4 Change of Variables 20
Exercises 21
Mathematical Modeling 23
Xin-She Yang
2.1 Mathematical Modeling 23
2.2 Model Formulation 25
2.3 Parameter Estimation 28
2.4 Mathematical Models 31
2.4.1 Differential Equations 31
2.4.2 Functional and Integral Equations 36
2.4.3 Statistical Models 36
2.4.4 Rule-based Models 40
2.5 Numerical Methods 40
2.5.1 Numerical Integration 40
2.5.2 Numerical Solutions of PDEs 41
Exercises 43
Numerical Methods: An Introduction 45
Xin-She Yang
3.1 Direct Integration 46
3.1.1 Euler Scheme 46
3.1.2 Leap-Frog Method 47
3.1.3 Runge-Kutta Method 48
3.2 Finite Difference Methods 49
3.2.1 Hyperbolic Equations 50
3.2.2 Second-Order Wave Equation 51
3.2.3 Parabolic Equation 52
3.2.4 Elliptical Equation 54
Exercises 55
Teaching Mathematical Modeling in Teacher Education: Efforts
and Results 57
Thomas Lingefjard
4.1 Introduction 57
4.2 Theoretical Frameworks Connected to Mathematical
Modeling 60
4.2.1 Instrumental Competence 61
4.2.2 The Importance of Variation 63
4.3 Mathematical Modeling Tasks 64
4.4 Conclusions 77
Exercises 77
PART II MATHEMATICAL MODELING WITH
MULTIDISCIPLINARY APPLICATIONS
5 Industrial Mathematics with Applications 83
Alfredo Bermudez and Luz M. Garcia Garcia
5.1 Industrial Mathematics 84
5.2 Numerical Simulation of Metallurgical Electrodes 84
5.2.1 The Industrial Problem: Metallurgy of Silicon 84
5.2.2 Mathematical Modeling 88
5.2.3 Numerical Solution 95
5.2.4 Numerical Results 98
5.3 Numerical Simulation of Pit Lake Water Quality 99
5.3.1 Introduction to the Problem 99
5.3.2 A Stirred Tank Model to Predict Pit Lake Water
Quality 102
5.3.3 Mathematical Models for Chemical Reaction
Systems 106
5.3.4 Numerical Solution of the Model 115
5.3.5 Numerical Results: A Simplified Chemical
Problem. 116
Exercises 120
6 Binary and Ordinal Data Analysis in Economics: Modeling and
Estimation 123
Ivan Jeliazkov and Mohammad Arshad Rahman
6.1 Introduction 123
6.2 Theoretical Foundations 124
6.2.1 Binary Outcomes 125
6.2.2 Ordinal Outcomes 129
6.3 Estimation 132
6.3.1 Maximum Likelihood Estimation 132
6.3.2 Bayesian Estimation 135
6.3.3 Marginal Effects 143
6.4 Applications 145
6.4.1 Women s Labor Force Participation 145
6.4.2 An Ordinal Model of Educational Attainment 146
6.5 Conclusions 147
Exercises 148
Inverse Problems in ODEs 151
H. Kunze and D. La Torre
7.1 Banach s Fixed Point Theorem The Collage Theorem 152
7.2 Existence-Uniqueness of Solutions to Initial Value
Problems 157
7.3 Solving Inverse Problems for ODEs 160
Exercises 166
References 167
Estimation of Model Parameters 169
Robert Piche
8.1 Estimation is an Inverse Problem 169
8.2 The Multivariate Normal Distribution 171
8.3 Model of Observations 174
8.3.1 Deterministic Model and its Linearization 174
8.3.2 Probabilistic Model 177
8.4 Estimation 178
8.4.1 Bayesian Inference 178
8.4.2 Moment Matching 178
8.4.3 Estimation by Optimization 184
8.5 Conclusion 188
Exercises 189
Linear and Nonlinear Parabolic Partial Differential Equations in
Financial Engineering 191
L. A. Boukas, K. I. Vasileiadis, S. Z. Xanthopoulos, A. N. Yannacopoulos
9.1 Financial Derivatives 191
9.2 Motivation for a Model for the Price of Stocks 194
9.3 Stock Prices Involving the Wiener Process 195
9.4 Connection Between the Wiener Process and PDEs 199
9.5 The Black-Scholes-Merton Equation 201
9.6 Solution of the Black-Scholes-Merton Equation 203
9.7 Free Boundary-Value Problems 204
9.8 The Hamilton-Jacobi-Bellman Equation 208
9.8.1 The Hamilton-Jacobi-Bellman Equation 211
9.8.2 An Explicitly Worked Example 216
9.8.3 Viscosity Solutions 218
9.9 Numerical Methods 220
9.9.1 The Crank-Nicholson Method 220
9.9.2 Numerical Treatment of Variational Inequalities 224
9.9.3 Numerical Treatment of HJB Equations 225
9.10 Conclusion 226
Exercises 226
10 Decision Modeling in Supply Chain Management 229
Huajun Tang
10.1 Introduction to Decision Modeling 229
10.1.1 The Origin of Decision Modeling 229
10.1.2 Definition of Decision Modeling 230
10.1.3 Data in Decision Modeling 230
10.1.4 Role of Spreadsheets in Decision Modeling 230
10.1.5 Types of Decision Models 231
10.1.6 Steps of Decision Modeling 231
10.2 Mathematical Programming Models 234
10.2.1 Introduction of Linear Programming Models 234
10.2.2 Properties of a Linear Programming Model 234
10.2.3 Assumptions of a Linear Programming Model 235
10.2.4 Other Mathematical Programming Models 236
10.3 Introduction of Supply Chain Management 236
10.3.1 Importance of Supply Chain Management 237
10.3.2 Activities in Supply Chain Management 238
10.4 Applications in Supply Chain Management 238
10.4.1 Manufacturing Applications 238
10.4.2 Transportation Applications 242
10.4.3 Assignment Applications 248
10.5 Summary 252
Exercises 253
11 Modeling Temperature for Pricing Weather Derivatives 257
Fred Espen Benth
11.1 Introduction 257
11.2 Stochastic Temperature Modeling 259
11.2.1 Simple Stochastic Mean Reverting Processes 261
11.3 Continuous-Time Autoregressive Processes 267
11.3.1 An Empirical Study 274
11.4 Pricing of Temperature Futures Contracts 277
Exercises 283
12 Decision Theory under Risk and Applications in Social Sciences:
I. Individual Decision Making 285
E. V. Petracou and A. N. Yannacopoulos
12.1 Introduction 285
12.2 The Fundamental Framework 286
12.3 A Brief Introduction to Theory of Choice 290
12.4 Collective Choice 292
12.5 Preferences Under Uncertainty 293
12.6 Decisions Over Time 299
12.7 The Problem of Aggregation 301
12.7.1 Aggregation of Time Preferences 301
12.7.2 Aggregation of Beliefs 303
12.8 Conclusion 304
Exercises 305
13 Fractals, with Applications to Signal and Image Modeling 307
H. Kunze and D. La Torre
13.1 Iterated Function Systems 308
13.2 Fractal Dimension 310
13.3 More on the Definition of Iterated Function System 312
13.4 The Chaos Game 314
13.5 An Application to Image Analysis 320
References 327
14 Efficient Numerical Methods for Singularly Perturbed Differential
Equations 329
S. Natesan
14.1 Introduction 329
14.2 Characterization of SPPs 331
14.3 Numerical Approximate Solution 333
14.3.1 Failure of Classical Finite Difference Schemes on
Uniform Meshes 333
14.3.2 Exponentially Fitted Difference Scheme 335
14.4 SPPs Arising in Chemical Reactor Theory 337
14.4.1 Initial-Value Technique 338
14.4.2 Boundary-Value Technique 340
14.4.3 Shooting Method 343
14.4.4 Booster Method 345
14.4.5 Semilinear Problems 347
14.5 Layer-Adapted Nonuniform Meshes 349
14.5.1 Bakhvalov Meshes 349
14.5.2 Shishkin Meshes 350
14.5.3 Equidistribution Meshes 351
PART III ADVANCED MODELING TOPICS
15 Fractional Calculus and its Applications 357
Ivo Petras
15.1 Introduction 357
15.2 Fractional Calculus Fundamentals 359
15.2.1 Special Functions 359
15.2.2 Definitions of Fractional Operator 359
15.2.3 Griinwald-Letnikov Fractional Derivatives 360
15.2.4 Riemann-Liouville Fractional Derivatives 360
15.2.5 Caputo Fractional Derivatives 360
15.2.6 Laplace Transform Method 361
15.2.7 Some Properties of Fractional Calculus 361
15.2.8 Numerical Methods for Fractional Calculus 362
15.3 Fractional-Order Systems and Controllers 370
15.3.1 Fractional LTI Systems 370
15.3.2 Fractional Nonlinear Systems 373
15.3.3 Fractional-Order Controllers 373
15.4 Stability of Fractional-Order Systems 374
15.4.1 Stability of Fractional LTI Systems 379
15.4.2 Stability of Fractional Nonlinear Systems 382
15.5 Applications of Fractional Calculus 385
15.5.1 Control of Electrical Heater 385
15.5.2 Memristor-Based Chua s Circuit 387
15.5.3 Viscoelastic Models of Cells 391
Exercises 393
16 The Goal Programming Model: Theory and Applications 397
Belaid Aouni, Cinzia Colapinto, and Davide La Torre
16.1 Multi-Criteria Decision Aid 397
16.2 The Goal Programming Model 399
16.3 Scenario-based Goal Programming 402
16.4 Applications 404
16.4.1 A Goal Programming Model for Portfolio Selection 404
16.4.2 A Goal Programming Model for Media
Management and Planning 407
16.4.3 A Goal Programming Model for Site Selection 410
16.4.4 A Goal Programming Model for the Next Release
Problem 412
Exercises 416
17 Decision Theory under Risk and Applications in Social Sciences:
II. Game Theory 421
E. V. Petracou and A. N. Yannacopoulos
17.1 Introduction 421
17.2 Best Replies and Nash Equilibria 422
17.3 Mixed Strategies and Minimax 428
17.4 Nash Equilibria and Conservative Strategies 430
17.5 Zero-Sum Games and the Minimax Theorem 432
17.6 Nash Equilibria for Mixed Strategies 438
17.7 Cooperative Games 440
17.8 Conclusion 446
Exercises 446
18 Control Problems on Differential Equations 449
Chuang Zheng
18.1 Introduction 449
18.2 Ordinary Differential Equations 451
18.2.1 Model Formulation 451
18.2.2 Controllability 454
18.2.3 Kalman s Rank Condition 457
18.3 Partial Differential Equations 460
18.3.1 Model Formulation 460
18.3.2 Controllability 463
18.3.3 Adjoint System and Observability 465
Exercises 469
19 Markov-Jump Stochastic Models for Tropical Convection 471
Boualem Khouider
19.1 Introduction 471
19.2 Random Numbers: Theory and Simulations 475
19.2.1 Random Variables 475
19.2.2 Mean, Variance, and Expectation 478
19.2.3 Conditional Probability 479
19.2.4 Law of Large Numbers 480
19.2.5 Monte Carlo Integration 481
19.2.6 Inverse Transform Method 483
19.2.7 Acceptance-Rejection Method 485
19.3 Markov Chains and Birth-Death Processes 486
19.3.1 Discrete-Time Markov Chains 487
19.3.2 The Poisson Process 489
19.3.3 Continuous-Time Markov Chains 491
19.4 A Birth-Death Process for Convective Inhibition 495
19.4.1 The Microscopic Stochastic Model for CIN: Ising
Model 495
19.4.2 The Coarse-Grained Mesoscopic Stochastic Model:
Birth-Death Process 499
19.4.3 Acceptance-Rejection Algorithm for the Birth-
Death Markov Process 502
19.4.4 Gillespie s Exact Algorithm 503
19.4.5 Numerical Tests 503
19.5 A Birth-Death Process for Cloud-Cloud Interactions 504
19.5.1 The Stationary Distribution, Cloud Area
Fractions, and the Equilibrium Statistics of the
Lattice Model 510
19.5.2 Coarse-Grained Birth-Death Stochastic Model
and the Mean-Field Equations 512
19.5.3 The Deterministic Mean-Field Equations and
Numerical Simulations 516
19.6 Further Reading 517
Exercises 519
Problem Solutions 525
Index 555
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| spelling | Mathematical modeling with multidisciplinary applications ed. by Xin-She Yang Hoboken, NJ Wiley 2013 XXXI, 557 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturangaben "This book details the interdisciplinary nature of mathematical modeling and numerical algorithms. It combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Including case studies, worked examples, and exercises, it cover topics such as partial differential equations, fractional calculus, inverse problems by ODEs, semigroups, decision theory, risk analysis, Bayesian estimation, nonlinear PDEs in financial engineering, perturbation analysis, dynamic system modeling, and much more"-- Mathematisches Modell Differential equations Mathematical models Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Mathematische Modellierung (DE-588)7651795-0 s DE-604 Yang, Xin-She 1965- (DE-588)1043733906 edt http://www.loc.gov/catdir/enhancements/fy1210/2012020899-d.html 80 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025908157&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematical modeling with multidisciplinary applications Mathematisches Modell Differential equations Mathematical models Mathematische Modellierung (DE-588)7651795-0 gnd |
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| title | Mathematical modeling with multidisciplinary applications |
| title_auth | Mathematical modeling with multidisciplinary applications |
| title_exact_search | Mathematical modeling with multidisciplinary applications |
| title_full | Mathematical modeling with multidisciplinary applications ed. by Xin-She Yang |
| title_fullStr | Mathematical modeling with multidisciplinary applications ed. by Xin-She Yang |
| title_full_unstemmed | Mathematical modeling with multidisciplinary applications ed. by Xin-She Yang |
| title_short | Mathematical modeling with multidisciplinary applications |
| title_sort | mathematical modeling with multidisciplinary applications |
| topic | Mathematisches Modell Differential equations Mathematical models Mathematische Modellierung (DE-588)7651795-0 gnd |
| topic_facet | Mathematisches Modell Differential equations Mathematical models Mathematische Modellierung Aufsatzsammlung |
| url | http://www.loc.gov/catdir/enhancements/fy1210/2012020899-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025908157&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT yangxinshe mathematicalmodelingwithmultidisciplinaryapplications |