Book:B. Noble/Numerical Methods/Volume 2

B. Noble: Numerical Methods, Volume $\text { II }$

Published $\text {1964}$, Oliver and Boyd Ltd

Subject Matter

• Numerical Analysis

Contents

A Note for the Reader

Volume $\text {II}$. -- DIFFERENCES, INTEGRATION AND DIFFERENTIAL EQUATIONS

$\text {VII}$. Finite Differences and the Approximate Representation of Functions

7.1 Introduction

7.2 Finite difference tables

7.3 The use of differences in detecting errors

7.4 The differences of a polynomial

7.5 The approximate representation of functions

Examples $\text {VII}$

$\text {VIII}$. Polynomial Interpolation

8.1 Introduction

8.2 Errors in polynomial interpolation

8.3 Aitken's method of interpolation by linear crossmeans

8.4 Newton's divided-difference interpolation formula

8.5 The Gregory-Newton and the Gauss formulae

8.6 The Everett, Bessel, and Stirling formulae

8.7 Practical interpolation using differences

Examples $\text {VIII}$

$\text {IX}$. Numerical Integration and Differentiation

9.1 Introduction

9.2 The trapezoidal rule and Simpson's rule

9.3 Error estimation: Simpson's rule in hand and automatic computing

9.4 The treatment of singularities

9.5 Gaussian formulae

9.6 Central difference formulae

9.7 Numerical differentiation

Examples $\text {IX}$

$\text {X}$. Ordinary Differential Equations

10.1 Introduction

10.2 Elementary considerations

10.3 Error estimation when solving differential equations numerically

10.4 Programming the numerical solution of differential equations

10.5 Runge-Kutta formulae

10.6 Predictor-corrector methods

10.7 Errors and stability

10.8 A comparison of methods

10.9 Second-order equations

10.10 Two-point boundary conditions

Examples $\text {X}$

$\text {XI}$. Partial Differential Equations

11.1 Introduction

11.2 The heat conduction equation

11.3 Laplace's equation

Examples $\text {XI}$

Index

Also see

• 1964: B. Noble: Numerical Methods: Volume $\text { 1 }$