Mathematical Modeling with Multidisciplinary Applications

CHAPTER 2

MATHEMATICAL MODELING

XIN-SHE YANG

School of Science and Technology, Middlesex University, London, UK

Also Mathematics and Scientific Computing, National Physical Laboratory, UK

2.1 MATHEMATICAL MODELING

Mathematical modeling is the process of formulating an abstract model in terms of mathematical language to describe the complex behavior of a real system. Mathematical models are quantitative models and often expressed in terms of ordinary differential equations and partial differential equations. Mathematical models can also be statistical models, fuzzy logic models and empirical relationships. In fact, any model description using mathematical language can be called a mathematical model. Mathematical modeling is widely used in natural sciences, computing, engineering, meteorology, and industrial applications. For example, theoretical physics is essentially all about the modeling of real world processes using several basic principles (such as the conservation of energy, momentum) and a dozen important equations (such as the wave equation, the Schrödinger equation, the Einstein equation). Almost all these equations are partial differential equations (PDEs).

An important feature of mathematical modeling and numerical algorithms is its interdisciplinary nature. It involves applied mathematics, computer sciences, physical and biological sciences, and others. Mathematical modeling in combination with scientific computing is an emerging interdisciplinary technology. Many international ...