# Book:B. Noble/Numerical Methods/Volume 2

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

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

### 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