E-Book, Englisch, 252 Seiten, Web PDF
Wendroff Theoretical Numerical Analysis
1. Auflage 2014
ISBN: 978-1-4832-7522-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 252 Seiten, Web PDF
ISBN: 978-1-4832-7522-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Theoretical Numerical Analysis focuses on the presentation of numerical analysis as a legitimate branch of mathematics. The publication first elaborates on interpolation and quadrature and approximation. Discussions focus on the degree of approximation by polynomials, Chebyshev approximation, orthogonal polynomials and Gaussian quadrature, approximation by interpolation, nonanalytic interpolation and associated quadrature, and Hermite interpolation. The text then ponders on ordinary differential equations and solutions of equations. Topics include iterative methods for nonlinear systems, matrix eigenvalue problems, matrix inversion by triangular decomposition, homogeneous boundary value problems, and initial value problems. The publication takes a look at partial differential equations, including heat equation, stability, maximum principle, and first order systems. The manuscript is a vital source of data for mathematicians and researchers interested in theoretical numerical analysis.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Theoretical Numerical Analysis;4
3;Copyright Page;5
4;Table of Contents;10
5;Preface;8
6;Preliminaries;12
7;THEORETICAL NUMERICAL ANALYSIS;14
8;Chapter 1. Interpolation and Quadrature;16
8.1;1.1. HERMITE INTERPOLATION;16
8.2;1.2. LAGRANGE INTERPOLATION AND NEWTON-COTES QUADRATURE;22
8.3;1.3. ORTHOGONAL POLYNOMIALS AND GAUSSIAN QUADRATURE;29
8.4;1.4. NONANALYTIC INTERPOLATION AND ASSOCIATED QUADRATURE;38
8.5;EXERCISES;47
8.6;COMPUTER PROBLEMS;48
8.7;NOTES;48
9;Chapter 2. Approximation;50
9.1;2.1. DEGREE OF APPROXIMATION BY POLYNOMIALS;50
9.2;2.2 APPROXIMATION BY INTERPOLATION;59
9.3;2.3. CHEBYSHEV APPROXIMATION;69
9.4;2.4. AN ALGORITHM FOR CHEBYSHEV APPROXIMATION;76
9.5;APPENDIX;82
9.6;EXERCISES;86
9.7;COMPUTER PROBLEMS;88
9.8;NOTES;88
10;Chapter 3. Ordinary Differential Equations;89
10.1;3.1. THE INITIAL VALUE PROBLEM;90
10.2;3.2. AN INHOMOGENEOUS BOUNDARY VALUE PROBLEM;101
10.3;3.3. A HOMOGENEOUS BOUNDARY VALUE PROBLEM;111
10.4;EXERCISES;121
10.5;COMPUTER PROBLEMS;123
10.6;NOTES;123
11;Chapter 4. Solution of Equations;125
11.1;4.1. MATRIX INVERSION BY TRIANGULAR DECOMPOSITION;126
11.2;4.2. THE MATRIX EIGENVALUE PROBLEM;150
11.3;4.3. LINEAR ITERATIVE METHODS;168
11.4;4.4. ITERATIVE METHODS FOR NONLINEAR SYSTEMS;176
11.5;EXERCISES;190
11.6;COMPUTER PROBLEM;192
11.7;NOTES;192
12;Chapter 5. Partial Differential Equations;194
12.1;5.1. FIRST ORDER SYSTEMS;195
12.2;5.2. THE HEAT EQUATION;209
12.3;5.3. STABILITY;217
12.4;5.4. THE MAXIMUM PRINCIPLE;238
12.5;EXERCISES;245
12.6;NOTES;246
13;References;247
14;Additional Reading;250
15;AUTHOR INDEX;252
16;SUBJECT INDEX;253
