ProofWiki:Books/B. Noble/Numerical Methods 2: Differences, Integration and Differential Equations

B. Noble: Numerical Methods 2: Differences, Integration and Differential Equations

Published 1964, Oliver and Boyd Ltd.

Subject Matter

• Numerical Analysis

Contents

A NOTE FOR THE READER

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 VII

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 VIII

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 IX

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 X

XI. PARTIAL DIFFERENTIAL EQUATIONS

11.1 Introduction

11.2 The heat conduction equation

11.3 Laplace's equation

Examples XI

INDEX