Numerical Modeling in Science and Engineering

A unified approach to numerical modelling which integrates aspects of continuum mechanics, differential equations, and numerical analysis, is presented in this book. The text is an explanation how to formulate a mathematical description of the phenomena under consideration, devise techniques for solving the governing equations, then refine the model and interpret the results. Emphasis is put on physical applications, and the three major classes of partial differential equations - elliptic, parabolic and hyperbolic - are related to steady-state systems, dissipative systems, and nondissipative systems, respectively. Some higher-order equations, nonlinear equations, and coupled systems of equations are also examined.