Book:B. Noble/Numerical Methods/Volume 2

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