Khabaza / Arscott Numerical Analysis

The Commonwealth and International Library: Higher Mathematics for Scientists and Engineers
1. Auflage 2014
ISBN: 978-1-4831-3956-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 254 Seiten, Web PDF

Numerical Analysis is an elementary introduction to numerical analysis, its applications, limitations, and pitfalls. Methods suitable for digital computers are emphasized, but some desk computations are also described. Topics covered range from the use of digital computers in numerical work to errors in computations using desk machines, finite difference methods, and numerical solution of ordinary differential equations. This book is comprised of eight chapters and begins with an overview of the importance of digital computers in numerical analysis, followed by a discussion on errors in computations using desk machines. Subsequent chapters deal with recurrence relations and algebraic equations; basic properties of matrices; relaxation and finite difference methods; and numerical methods for unequal intervals. The derivation of Lagrange's interpolation polynomial is explained, together with curve fitting and the method of least squares, orthogonal polynomials, and integration methods. This monograph will be of interest to practicing engineers, mathematicians, and scientists as well as students.

Autoren/Hrsg.

Khabaza, I. M.

Arscott, F. M.

Inhaltsverzeichnis

1;Front Cover;1
2;Numerical Analysis;4
3;Copyright Page;5
4;Table of Contents;6
5;Foreword;8
6;Preface;12
7;Suggestions for further reading;13
8;Chapter 1. DIGITAL COMPUTERS;14
8.1;1.1 General description;14
8.2;1.2 Input and output systems;15
8.3;1.3 Storage systems;16
8.4;1.4 Arithmetic unit;17
8.5;1.5 The control unit;20
8.6;1.6 Some general programming concepts;23
9;Chapter 2. DESK MACHINES ERRORS IN COMPUTATIONS;26
9.1;2.1 Basic operations on desk machines;26
9.2;2.2 Further techniques on desk machines;29
9.3;2.3 Types of errors in computations. Error analysis;32
9.4;2.4 Rounding errors and accuracy;34
9.5;2.5 Checks;39
9.6;Exercises;41
10;Chapter 3. FINITE-DIFFERENCE METHODS;43
10.1;3.1 Difference tables;43
10.2;3.2 Differencing polynomials: Errors in difference tables;49
10.3;3.3 Interpolation;52
10.4;3.4 Inverse interpolation;55
10.5;3.5 Backward differences;58
10.6;3.6 Central differences;60
10.7;3.7 Central-difference interpolation formulae;62
10.8;3.8 Differentiation formulae;68
10.9;3.9 Integration;71
10.10;3.10 Derivation of the central-difference interpolation formulae;82
10.11;3.11 Concluding remarks;86
10.12;Exercises;87
11;Chapter 4. RECURRENCE RELATIONS AND ALGEBRAICEQUATIONS;90
11.1;4.1 Recurrence relations: difference equations;90
11.2;4.2 Summation of series;98
11.3;4.3 Bernoulli's method for solving polynomial equations;103
11.4;4.4 Newton-Raphson method. Order of convergence of an iterativeprocedure;108
11.5;4.5 Graeffe's root-squaring method;113
11.6;4.6 The methods of Lin and Bairstow;115
11.7;Exercises;121
12;Chapter 5. NUMERICAL SOLUTION OF ORDINARY DIFFERENTIALEQUATIONS;123
12.1;5.1 Predictor-corrector methods;129
12.2;5.2 Single-step methods;129
12.3;5.3 Systems of differential equationsDifferential equations of order higher than 1;131
12.4;5.4 Further methods;134
12.5;5.5 Accuracy. Error build-up;139
12.6;5.6 Solution of differential equations on digital computers Exercises;145
13;Chapter 6. MATRICES;149
13.1;6.1 Elementary properties;149
13.2;6.2 Solution of sets of linear equations by elimination;158
13.3;6.3 Solution of sets of linear equations on desk machines;167
13.4;6.4 Latent roots and vectors;174
13.5;Exercises;188
14;Chapter 7. RELAXATION METHODS;191
14.1;7.1 Solution of linear equations;191
14.2;7.2 Second order ordinary differential equations with two-pointboundary conditions;197
14.3;7.3 Solution of partial differential equations of the Poisson type Exercises;208
14.4;Exercises;218
15;Chapter 8. NUMERICAL METHODS FOR UNEQUAL INTERVALS;220
15.1;8.1 Interpolation;220
15.2;8.2 Curve fitting and the method of least squares;230
15.3;8.3 Orthogonal polynomials;236
15.4;8.4 Integration;247
15.5;Exercises;250
16;INDEX;254