Numerical Methods for Nonlinear Engineering Models

ISBN-13: 9789401777070 / Angielski / Miękka / 2017 / 1013 str.

John R. Hauser

Opis

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.

Recenzje

From the reviews:

"This voluminous book by Hauser ... covers numerical topics ranging from roots of nonlinear equations to introductory finite element method. The advantage of this work lies in the author's approach of show-and-tell or 'learning by example.' ... The examples are almost exclusively in the area of nonlinear electronics ... which may be quite advantageous for electronics engineers. ... Summing Up: Recommended. Upper-division undergraduate through professional collections." (R. N. Laoulache, Choice, Vol. 47 (3), November, 2009)

"The book represents a comprehensive guide for the exploitation of standard numerical tools in nonlinear engineering problems. The presentation style ensures a balanced construction in providing mathematical knowledge illustrated by relevant examples. ... suitable for self-study and teaching support at the first postgraduate level. The book is recommended to educators interested in preparing or upgrading lecture notes and seminars, students specializing in different fields of engineering, and practitioners working with various types of nonlinear models." (Octavian Pastravanu, Zentralblatt MATH, Vol. 1173, 2009)

Spis treści

Preface; 1 Introduction to Nonlinear Engineering Problems and Models; 1.1 Science and Engineering ; 1.2 The Engineering Method; 1.3 Some General Features of Engineering Models ; 1.4 Linear and Nonlinear; 1.5 A Brief Look Ahead ; 2 Numerical Fundamentals and Computer Programming; 2.1 Computer Programming Languages; 2.2 Lua as a Programming Language; 2.3 Data Representation and Associated Limitations; 2.4 Language Extensibility; 2.5 Some Language Enhancement Functions; 2.6 Software Coding Practices; 2.7 Summary; 3 Roots of Nonlinear Equations; 3.1 Successive Substitutions or Fixed Point Iteration; 3.2 Newton’s Method or Newton-Ralphson Method; 3.3 Halley’s Iteration Method; 3.4 Other Solution Methods; 3.5 Some Final Considerations for Finding Roots of Functions; 3.6 Summary; 4 Solving Sets of Equations: Linear and Nonlinear; 4.1 The Solution of Sets of Linear Equations; 4.2 Solution of Sets of Nonlinear Equations; 4.3 Some Examples of Sets of Equations; 4.4 Polynomial Equations and Roots of Polynomial Equations; 4.5 Matrix Equations and Matrix Operations; 4.6 Matrix Eigenvalue Problems; 4.7 Summary; 5 Numerical Derivatives and Numerical Integration; 5.1 Fundamentals of Numerical Derivatives; 5.2 Maximum and Minimum Problems; 5.3 Numerical Partial Derivatives and Min/Max Applications; 5.4 Fundamentals of Numerical Integration; 5.5 Integrals with Singularities and Infinite Limits; 5.6 Summary; 6 Interpolation; 6.1 Introduction to Interpolation – Linear Interpolation; 6.2 Interpolation using Local Cubic (LCB) Functions; 6.3 Interpolation using Cubic Spline Functions (CSP); 6.4 Interpolation Examples with Known Functions; 6.5 Interpolation Examples with Unknown Functions; 6.6 Summary; 7 Curve Fitting and Data Plotting; 7.1 Introduction; 7.2 Linear Least Squares Data Fitting; 7.3 General Least Squares Fitting with Linear Coefficients; 7.4 The Fourier Series Method; 7.5 Nonlinear Least Squares Curve Fitting; 7.6 Data Fitting and Plotting with Known Functional Foms;7.7 General Data Fitting and Plotting; 7.8 Rational Function Approximations to Implicit Functions; 7.9 Weighting Factors; 7.10 Summary; 8 Statistical Methods and Basic Statistical Functions; 8.1 Introduction; 8.2 Basic Statistical Properties and Functions; 8.3 Distributions and More Distributions; 8.4 Analysis of Mean and Variance; 8.5 Comparing Distribution Functions – The Kolmogorov-Smirnov Test; 8.6 Monte Carlo Simulations and Confidence Limits; 8.7 Non-Gaussian Distributions and Reliability Modeling ; 8.8 Summary; 9 Data Models and Parameter Estimation; 9.1 Introduction; 9.2 Goodness of Data Fit and the 6-Plot Approach; 9.3 Confidence Limits on Estimated Parameters and MC Analysis; 9.4 Examples of Single Variable Data Fitting and Parameter Estimation; 9.5 Data Fitting and Parameter Estimation with Weighting Factors; 9.6 Data Fitting and Parameter Estimation with Transcendental Functions; 9.7 Data Fitting and Parameter Estimation with Piecewise Model Equations; 9.8 Data Fitting and Parameter Estimation with Multiple Independent Parameters; 9.9 Response Surface Modeling and Parameter Estimation; 9.10 Summary; 10 Differential Equations: Initial Value Problems; 10.1 Introduction to the Numerical Solution of Differential Equations; 10.2 Systems of Differential Equations; 10.3 Exploring Stability and Accuracy Issues with Simple Examples; 10.4 Development of a General Differential Equation Algorithm; 10.5 Variable Time Step Solutions; 10.6 A More Detailed Look at Accuracy Issues with the TP Algorithm; 10.7 Runge-Kutta Algorithms; 10.8 An Adaptive Step Size Algorithm; 10.9 Comparison with MATLAB Differential Equation Routines; 10.10 Direct Solution of Second Order Differential Equations; 10.11 Differential-Algebraic Systems of Equations; 10.12 Examples of Initial Value Problems; 10.13 Summary; 11 Differential Equations: Boundary Value Problems ; 11.1 Introduction to Boundary Value Problems in One Independent Variable; 11.2 Shooting(ST) Methods and Boundary Value

Blurb

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.