Numerical Analysis

Numerical Analysis

The Commonwealth and International Library: Higher Mathematics for Scientists and Engineers

1st Edition - January 1, 1965

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  • Author: I. M. Khabaza
  • eBook ISBN: 9781483139562

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Description

Numerical Analysis is an elementary introduction to numerical analysis, its applications, limitations, and pitfalls. Methods suitable for digital computers are emphasized, but some desk computations are also described. Topics covered range from the use of digital computers in numerical work to errors in computations using desk machines, finite difference methods, and numerical solution of ordinary differential equations. This book is comprised of eight chapters and begins with an overview of the importance of digital computers in numerical analysis, followed by a discussion on errors in computations using desk machines. Subsequent chapters deal with recurrence relations and algebraic equations; basic properties of matrices; relaxation and finite difference methods; and numerical methods for unequal intervals. The derivation of Lagrange's interpolation polynomial is explained, together with curve fitting and the method of least squares, orthogonal polynomials, and integration methods. This monograph will be of interest to practicing engineers, mathematicians, and scientists as well as students.

Table of Contents


  • Foreword

    Preface

    Suggestions for Further Reading

    1. Digital Computers

    1.1 General Description

    1.2 Input and Output Systems

    1.3 Storage Systems

    1.4 Arithmetic Unit

    1.5 The Control Unit

    1.6 Some General Programming Concepts

    2. Desk Machines. Errors in Computations

    2.1 Basic Operations on Desk Machines

    2.2 Further Techniques on Desk Machines

    2.3 Types of Errors in Computations. Error Analysis

    2.4 Rounding Errors and Accuracy

    2.5 Checks

    Exercises

    3. Finite-Difference Methods

    3.1 Difference Tables

    3.2 Differencing Polynomials: Errors in Difference Tables

    3.3 Interpolation

    3.4 Inverse Interpolation

    3.5 Backward Differences

    3.6 Central Differences

    3.7 Central-Difference Interpolation Formulae

    3.8 Differentiation Formulae

    3.9 Integration

    3.10 Derivation of the Central-Difference Interpolation Formulae

    3.11 Concluding Remarks

    Exercises

    4. Recurrence Relations and Algebraic Equations

    4.1 Recurrence Relations: Difference Equations

    4.2 Summation of Series

    4.3 Bernoulli's Method for Solving Polynomial Equations

    4.4 Newton-Raphson Method. Order of Convergence of an Iterative Procedure

    4.5 Graeffe's Root-Squaring Method

    4.6 The Methods of Lin and Bairstow

    Exercises

    5. Numerical Solution of Ordinary Differential Equations

    5.1 Predictor-Corrector Methods

    5.2 Single-Step Methods

    5.3 Systems of Differential Equations. Differential Equations of Order Higher than 1

    5.4 Further Methods

    5.5 Accuracy. Error Build-Up

    5.6 Solution of Differential Equations on Digital Computers

    Exercises

    6. Matrices

    6.1 Elementary Properties

    6.2 Solution of Sets of Linear Equations by Elimination

    6.3 Solution of Sets of Linear Equations on Desk Machines

    6.4 Latent Roots and Vectors

    Exercises

    7. Relaxation Methods

    7.1 Solution of Linear Equations

    7.2 Second Order Ordinary Differential Equations with Two-Point Boundary Conditions

    7.3 Solution of Partial Differential Equations of the Poisson Type

    Exercises

    8. Numerical Methods for Unequal Intervals

    8.1 Interpolation

    8.2 Curve Fitting and the Method of Least Squares

    8.3 Orthogonal Polynomials

    8.4 Integration

    Exercises

    Index

Product details

  • No. of pages: 254
  • Language: English
  • Copyright: © Pergamon 1965
  • Published: January 1, 1965
  • Imprint: Pergamon
  • eBook ISBN: 9781483139562

About the Author

I. M. Khabaza

About the Editor

F. M. Arscott

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