Numerical Methods for Nonlinear Engineering Models

This book develops and illustrates some numerical computer-based methods that can be used for engineering models and equations. It emphasizes nonlinear engineering models and provides detailed discussion of computer algorithms for solving nonlinear problems.

There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.

The emphasis is on nonlinear engineering models and equations as opposed to linear models Linear models and equations are treated conveniently as just special cases of more general nonlinear models For each chapter and topic area covered, the theory is discussed and computer code is developed and presented such that the reader can conveniently apply the developed code to practical engineering problems For each topic covered at least one approach is extensively developed leading to working computer code that can be applied to nonlinear problems The computer code is developed in a modern scripting language that is very easy to program and understand by the reader

Klappentext

The purpose of this book is to develop and illustrate various numerical computer based methods that can be used for engineering models and equations. The intended audience is the practicing engineer who needs to model real world engineering models or the upper level engineering undergraduate or first year graduate student interested in developing skills in computer models of engineering problems. The material is presented in a "learning by example" style whereby many examples are used to develop and illustrate concepts as opposed to extensive mathematical treatments. The book presents an integrated approach to engineering models whereby linear models are treated as simple special cases of more general approaches appropriate for nonlinear models. In addition to standard topics in numerical methods, the material covers the estimation of parameters associated with engineering models and the statistical nature of modeling with nonlinear models. Topics covered include coupled systems of nonlinear equations and coupled systems of nonlinear differential equations.

For all the topics covered extensive computer code is developed in a modern computer language that is easy to program and understand. The developed code can be readily used to model real world engineering problems. Finally for all topic areas extensive discussion is included of the accuracy that can be achieved with the various numerical methods and methods are developed that can be used to access the accuracy of the modeling methods.

The book assumes only the normal mathematical background of the introductory college level mathematics courses through calculus. In addition the material can be readily understood by anyone familiar with at least one computer programming language.

Inhalt
to Nonlinear Engineering Problems and Models.- Numerical Fundamentals and Computer Programming.- Roots of Nonlinear Equations.- Solving Sets of Equations: Linear and Nonlinear.- Numerical Derivatives and Numerical Integration.- Interpolation.- Curve Fitting and Data Plotting.- Statistical Methods and Basic Statistical Functions.- Data Models and Parameter Estimation.- Differential Equations: Initial Value Problems.- Differential Equations: Boundary Value Problems.- Partial Differential Equations: Finite Difference Approaches.- Partial Differential Equations: The Finite Element Method.