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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.
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.
Table of Contents
List of Figures xv
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