A Practical Guide to Computer Methods for Engineers - Terry E. Shoup - Hardcover

A Practical Guide to Computer Methods for Engineers by Terry E. Shoup

Publisher: Prentice Hall /
Year: 1979, First printing./
ISBN: 0136906516 /
Description: Hardcover without dust jacket, Good condition /
Condition: Ex-library with no exterior library marks, no underlining, no highlighting /
Pages: 255 pages

PREFACE

The present revolution in size, cost and capability of modern computational equipment has led to the application of computer methodology to a diversity of technological areas. With the increased emphasis on computer applications in engineering problem solving, more and more engineers are relying on the computer as a tool to assist them in their work. In most practical situations, the engineering programmer will build his or her program from the building blocks of available algorithms. This programming approach is based on sound judgment because it saves time and allows the engineer to exploit the computational talents of his or her computer science and mathematics colleagues. Although most practicing engineers and engineering students have a good working knowledge of computer programming, most are not well acquainted with the characteristics and limitations of the computer methods available to solve their problems. This book is aimed specifically at meeting this need--namely, to provide practical insight into selection of the best available algorithm to perform a given computational task. Unlike most texts in numerical methods, this book is written by an engineer specifically for use by engineers. The philosophy of presentation in this text begins with a clear, basic presentation of the fundamental algorithms. This is done with narrative, figures, logic flow diagrams, and example applications. Once the various algorithms are understood, they are compared and discussed with a view toward their unique advantages or limitations in a particular engineering situation. Whenever possible, available software is listed along with guidelines for practical application. A brief appendix of available computer software for engineering applications is presented at the end of the text.

CONTENTS

PREFACE

1 INTRODUCTION

1.1 Introduction to Computer-Aided Problem Solving 1
1.2 The Computer as a Tool in the Design Environment 2
1.3 Considerations in the Preparation of Engineering Programs 5
1.4 Computational Equipment for Engineering Problem Solving 5
1.5 Categories of Problems in Computer-Aided Engineering 7

2 COMPUTER SOLUTION OF ALGEBRAIC EQUATIONS

2.1 Introduction 10
2.2 Roots of a Single Nonlinear Equation 10
2.3 Solution of Polynomial Equations 20
2.4 Solution of Linear Simultaneous Equations 26
2.5 Solution of Nonlinear Simultaneous Algebraic Equations 31
2.6 Considerations in the Selection of a Method for the Solution Algebraic Systems 37
Problems 38

3 COMPUTER SOLUTION OF\' EIGENVALUE PROBLEMS

3.1 Introduction 44
3.2 Fundamentals of Eigenvalue Problems 44
3.3 Iterative Methods of Solution 46
3.4 Transform Methods of Eigenvalue Calculation 51
3.5 Finding the Eigenvalues of a Symmetric Tridiagonal Matrix 56
3.6 Other Methods of Eigenvalue Calculation 58
3.7 Considerations in the Selection of an Eigenvalue Algorithm 61
Problems 63

4 COMPUTER SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

4.1 Introduction 68
4.2 Categories of Ordinary Differential Equations 68
4.3 One-Step Methods for the Initial Value Problem 70
4.4 Predictor-Corrector Methods 81
4.5 Step Size Considerations 85
4.6 Stiff Problems 87
4.7 Methods for the Solution of Boundary-Value Problems 87
4.8 Considerations in the Selection of an Algorithm for Solving Ordinary Differential Equations 91
4.9 Available Packages for Modeling Engineering Systems 91
Problems 93

5 COMPUTER SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS

5.1 Introduction 100
5.2 Categories of Partial Differential Equations 100
5.3 Numerical Solution of Partial Differential Equation Problems by the Finite Difference Method 101
5.4 Grid Patterns for Use in Approximating Partial Differential Equations 103
5.5 Finite Difference Representations for Partial Derivatives 105
5.6 Iterative Solution Techniques 109
5.7 Parabolic Partial Differential Equations 117
5.8 Hyperbolic Partial Differential Equations 120
5.9 Numerical Solution of Partial Differential Equation Problems by the Finite Element Method 122
5.10 General Considerations in the Solution of Partial Differential Equations 128
Problems 129

6 OPTIMIZATION—PART I

6.1 Introduction 136
6.2 Fundamentals of Optimization 136
6.3 One-Dimensional Search Techniques 142
6.4 A Comparison of One-Dimensional Search Techniques 152
6.5 Available FORTRAN Codes for One-Dimensional Optimization 154
6.6 Summary 160 Problems 160

7 OPTIMIZATION—PART II

7.1 Multidimensional Search Techniques 166
7.2 Sectioning Method 166
7.3 Area Elimination 168
7.4 Random Search 170
7.5 Gradient Methods 172
7.6 Fletcher-Reeves Method 174
7.7 Davidon-Fletcher-Powell Method 179
7.8 Hooke and Jeeves Pattern Search 181
7.9 Rosenbrock Pattern Search 184
7.10 The Simplicial Method 186
7.11 Penalty Function Methods 189
7.12 Indirect Optimization 195
7.13 Considerations in the Selection of a Multidimensional Algorithm 198
7.14 FORTRAN Codes for Multidimensional Optimization 199
Problems 201

8 MISCELLANEOUS COMPUTER METHODS

8.1 Introduction 208
8.2 Interpolation 208
8.3 Curve Fitting 215
8.4 Numerical Differentiation 220
8.5 Numerical Integration 223
Problems 231

APPENDICES

A Computer Software for Engineering Applications 235
B Guidelines for Preparing Engineering Computer Programs 245
C Conversion Factors 247

INDEX
Optimization

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