Numerical Methods for Engineers: 2nd Edition (Hardback) book cover

Numerical Methods for Engineers

2nd Edition

By D. Vaughan Griffiths, I.M. Smith

Chapman and Hall/CRC

492 pages | 83 B/W Illus.

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pub: 2006-06-22
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Description

Although pseudocodes, Mathematica®, and MATLAB® illustrate how algorithms work, designers of engineering systems write the vast majority of large computer programs in the Fortran language. Using Fortran 95 to solve a range of practical engineering problems, Numerical Methods for Engineers, Second Edition provides an introduction to numerical methods, incorporating theory with concrete computing exercises and programmed examples of the techniques presented.

Covering a wide range of numerical applications that have immediate relevancy for engineers, the book describes forty-nine programs in Fortran 95. Many of the programs discussed use a sub-program library called nm_lib that holds twenty-three subroutines and functions. In addition, there is a precision module that controls the precision of calculations.

Well-respected in their field, the authors discuss a variety of numerical topics related to engineering. Some of the chapter features include…

  • The numerical solution of sets of linear algebraic equations

  • Roots of single nonlinear equations and sets of nonlinear equations

  • Numerical quadrature, or numerical evaluation of integrals

  • An introduction to the solution of partial differential equations using finite difference and finite element approaches

    Describing concise programs that are constructed using sub-programs wherever possible, this book presents many different contexts of numerical analysis, forming an excellent introduction to more comprehensive subroutine libraries such as the numerical algorithm group (NAG).

  • Table of Contents

    INTRODUCTION AND PROGRAMMING PRELIMINARIES

    Introduction

    Running Programs

    Hardware

    External Fortran Sub-Program Libraries

    A Simple Fortran Program

    Some Simple Fortran Constructs

    Intrinsic Functions

    User-Supplied Functions and Subroutines

    Errors and Accuracy

    Graphical Output

    Conclusions

    LINEAR ALGEBRAIC EQUATIONS

    Introduction

    Gaussian Elimination

    Equation Solution Using Factorization

    Equations with a Symmetrical Coefficient Matrix

    Banded Equations

    Compact Storage for Variable Bandwidths

    Pivoting

    Equations with Prescribed Solutions

    Iterative Methods

    Gradient Methods

    Unsymmetrical Systems

    Preconditioning

    Comparison of Direct and Iterative Methods

    Exercises

    NONLINEAR EQUATIONS

    Introduction

    Iterative Substitution

    Multiple Roots and Other Difficulties

    Interpolation Methods

    Extrapolation Methods

    Acceleration of Convergence

    Systems of Nonlinear Equations

    Exercises

    EIGENVALUE EQUATIONS

    Introduction

    Vector Iteration

    Intermediate Eigenvalues by Deflation

    The Generalized Eigenvalue Problem [K] {x} = ?[M] {x}

    Transformation Methods

    Characteristic Polynomial Methods

    Exercises

    INTERPOLATION AND CURVE FITTING

    Introduction

    Interpolating Polynomials

    Interpolation Using Cubic Spline Functions

    Numerical Differentiation

    Curve Fitting

    Exercises

    NUMERICAL INTEGRATION

    Introduction

    Newton-Cotes Rules

    Gauss-Legendre Rules

    Adaptive Integration Rules

    Special Integration Rules

    Multiple Integrals

    Exercises

    NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

    Introduction

    Definitions and Types of ODE

    Initial Value Problems

    Boundary Value Problems

    Exercises

    INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS

    Introduction

    Definitions and Types of PDE

    First Order Equations

    Second Order Equations

    Finite Difference Method

    Finite Element Method

    Exercises

    APPENDIX A: Descriptions of Library Subprograms

    APPENDIX B: Fortran 95 Listings of Library Subprograms

    APPENDIX C: References and Additional Reading

    Subject Categories

    BISAC Subject Codes/Headings:
    MAT003000
    MATHEMATICS / Applied
    MAT021000
    MATHEMATICS / Number Systems
    TEC009000
    TECHNOLOGY & ENGINEERING / Engineering (General)