Numerical Methods for Engineers / Edition 2

Numerical Methods for Engineers / Edition 2

by D. Vaughan Griffiths, I.M. Smith
     
 

ISBN-10: 1584884010

ISBN-13: 9781584884019

Pub. Date: 06/15/2006

Publisher: Taylor & Francis

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,

Overview

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).

  • Product Details

    ISBN-13:
    9781584884019
    Publisher:
    Taylor & Francis
    Publication date:
    06/15/2006
    Edition description:
    REV
    Pages:
    492
    Sales rank:
    1,134,190
    Product dimensions:
    6.00(w) x 9.30(h) x 1.30(d)

    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

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