Book:Alexander Graham/Numerical Analysis

Alexander Graham: Numerical Analysis

Published $\text {1973}$, Transworld Student Library

ISBN 0 552 40013 0

Subject Matter

• Numerical Analysis

Contents

Introduction

Notation used

chapter i Finite Differences

1.1 The forward difference operator

1.2 Some other operators and the relations between them

1.3 Differences of polynomial functions

1.4 Errors in difference tables

1.5 Interpolation formulae

1.6 The throwback technique

1.7 Numerical differentiation and integration

1.8 Some formulae for differentiation

1.9 Integration

chapter ii Lagrange Interpolation Polynomial and Divided Differences

2.1 Lagrange interpolation polynomial

2.2 Divided differences

2.3 Newton's interpolation formula with divided differences

2.4 Equally spaced tabular points

chapter iii Simultaneous Linear Equations

3.1 Direct methods

3.2 Computing the inverse of a matrix

3.3 Iterative methods

3.4 Rounding errors and ill-conditioning

3.5 Accumulation of errors in addition (and subtraction)

3.6 Accumulation of errors in multiplication (and division)

3.7 Errors in solving systems of simultaneous equations

chapter iv Numerical Solution of Differential Equations

4.1 Picard's method

4.2 A Taylor series method

4.3 Euler's method

4.4 The Adams-Bashforth method

4.5 The Runge-Kutta method

4.6 Differential equations of order higher than $1$

4.7 Accuracy and stability

chapter v Non-Linear Equations

5.1 Linear iterations

5.2 Quadratic iterations

5.3 Bairstow's method

Conclusion

Bibliography

Index

Next

Source work progress

• 1973: Alexander Graham: Numerical Analysis: $\text I$: Finite Differences: $1.1$ The forward difference operator