Mathematical Modeling With Multidisciplinary Applications

Features mathematical modeling techniques and real-world processes with applications in diverse fields

Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book 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.

Written by leading scholars and international experts in the field, the book presents new and emerging topics in areas including finance and economics, theoretical and applied mathematics, engineering and machine learning, physics, chemistry, ecology, and social science. In addition, the book thoroughly summarizes widely used mathematical and numerical methods in mathematical modeling and features:

• Diverse topics such as partial differential equations (PDEs), fractional calculus, inverse problems by ordinary differential equations (ODEs), semigroups, decision theory, risk analysis, Bayesian estimation, nonlinear PDEs in financial engineering, perturbation analysis, and dynamic system modeling
• Case studies and real-world applications that are widely used for current mathematical modeling courses, such as the green house effect and Stokes flow estimation
• Comprehensive coverage of a wide range of contemporary topics, such as game theory, statistical models, and analytical solutions to numerical methods
• Examples, exercises with select solutions, and detailed references to the latest literature to solidify comprehensive learning
• New techniques and applications with balanced coverage of PDEs, discrete models, statistics, fractional calculus, and more

Mathematical Modeling with Multidisciplinary Applications is an excellent book for courses on mathematical modeling and applied mathematics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for research scientists, mathematicians, and engineers who would like to develop further insights into essential mathematical tools.

XIN-SHE YANG, PhD, is Senior Research Scientist in the Department of Mathematical and Scientific Computing at the National Physical Laboratory in the United Kingdom, Reader in Modeling and Optimization at Middlesex University, UK, and Adjunct Professor at Reykjavik University, Iceland. He is Editor-in-Chief of the International Journal of Mathematical Modelling and Numerical Optimisation, a member of both the Society for Industrial and Applied Mathematics and the British Computer Society, a Fellow of The Royal Institution of Great Britain, and author of seven additional books and over 100 journal articles.

List of Figures xv

Preface xxv

Acknowledgments xxix

Part I. Introduction and Foundations

1. Differential Equations 3
Xin-She Yang

2. Mathematical Modelling 23
Xin-She Yang

3. Numerical Methods: An Introduction 45
Xin-She Yang

4. Teaching Mathematical Modelling 57
Thomas Lingefjärd

Part II. Mathematical Modelling with Multidisciplinary Applications

5. Industrial Mathematics with Applications 83
Alfredo Bermúdez and Luz M. García García

6. Data Analysis in Economics 123
Ivan Jeliazkov and Mohammad Arshad Rahman

7. Inverse Problems in ODEs 151
H. Kunze and D. La Torre

8. Estimation of Model Parameters 169
Robert Piché

9. Parabolic PDE in Financial Engineering 191
L. A. Boukas, K. I. Vasileiadis, S. Z. Xanthopoulos, A. N. Yannacopoulos

10. Decision Modeling in Supply Chain Management 229
Huajun Tang

11. Modelling Pricing Weather Derivatives 257
 Fred Espen Benth

12. Decision Theory in Social Sciences 285
E. V. Petracou and A. N. Yannacopoulos

13. Fractals, with applications to signal and image modeling 307
H. Kunze and D. La Torre

14. Efficient Numerical Methods for Singularly Perturbed Differential Equations 329
S. Natesan

Part III. Advanced Modelling Topics

15. Fractional Calculus and its Applications 357
Ivo Petráš

16. Goal Programming Model 397
Belaid Aouni, Cinzia Colapinto and Davide La Torre

17. Decision Theory and Game Theory 421
E. V. Petracou and A. N. Yannacopoulos

18. Control Problems on Differential Equations 449
Chuang Zheng

19. Markoc-jump stochastic models 473
Boualem Khouider

Problem Solutions 527

Index 559