<p>An unified approach to numerical modeling, integrating aspects of continuum mechanics, differential equations, and numerical analysis. Explains 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. Emphasizes physical applications and relates the three major classes of partial differential equations -- elliptic, parabolic, and hyperbolic -- to steady-state systems, dissipative systems, and nondissipative systems, respectively. Also examines some higher-order equations, nonlinear equations, and coupled systems of equations.</p>

Numerical Modeling in Science and Engineering

Science & Math

Pinder, George F.

Allen, Myron B.

Herrera, Ismael

Research

Wiley-Interscience

A powerful, unified approach to mathematical and computational modeling in science and engineering Mathematical and computational modeling makes it possible to predict the behavior of a broad range of systems across a broad range of disciplines. This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science. Readers will discover that this axiomatic approach not only enables them to systematically construct effective models, it also enables them to apply these models to any macroscopic physical system. Mathematical Modeling in Science and Engineering focuses on models in which the processes to be modeled are expressed as systems of partial differential equations. It begins with an introductory discussion of the axiomatic formulation of basic models, setting the foundation for further topics such as:   Mechanics of classical and non-classical continuous systems   Solute transport by a free fluid   Flow of a fluid in a porous medium   Multiphase systems   Enhanced oil recovery   Fluid mechanics   Throughout the text, diagrams are provided to help readers visualize and better understand complex mathematical concepts. A set of exercises at the end of each chapter enables readers to put their new modeling skills into practice. There is also a bibliography in each chapter to facilitate further investigation of individual topics. Mathematical Modeling in Science and Engineering is ideal for both students and professionals across the many disciplines of science and engineering that depend on mathematical and computational modeling to predict and understand complex systems.

Mathematical Modeling in Science and Engineering: An Axiomatic Approach

Mathematics

wiley

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