An introduction to numerical methods: a MATLAB approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Florida
CRC Press
[2019]
|
| Ausgabe: | Fourth edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes index |
| Beschreibung: | xv, 615 Seiten Diagramme |
| ISBN: | 9781138093072 1138093076 |
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| adam_text | Contents Preface xiii 1 Introduction 1.1 ABOUT MATLAB and MATLAB GUI (Graphical User Interface) 1.2 AN INTRODUCTION TO MATLAB................................................. 1.2.1 Matrices and matrix computation........................................... 1.2.2 Polynomials................................................................................ 1.2.3 Output format............................................................................. 1.2.4 Planar plots................................................................................ 1.2.5 3-D mesh plots .......................................................................... 1.2.6 Function files ............................................................................. 1.2.7 Defining functions....................................................................... 1.2.8 Relations and loops.................................................................... 1.3 TAYLOR SERIES................................................................................... 1 1 2 2 6 7 8 9 10 11 12 15 2 Number System and Errors 2.1 FLOATING-POINT ARITHMETIC ................................................. 2.2 ROUND-OFF ERRORS....................................................................... 2.3 TRUNCATION ERROR....................................................................... 2.4 INTERVAL ARITHMETIC................................................................. 23 23 28 32 34 3 Roots of Equations 3.1 THE BISECTION METHOD.............................................................. 3.2 FIXED POINT
ITERATION............................................................. 3.3 THE SECANT METHOD.................................................................... 3.4 NEWTON’S METHOD ....................................................................... 3.5 CONVERGENCE OF THE NEWTON AND SECANT METHODS............................................................................. 3.6 MULTIPLE ROOTS AND THE MODIFIED NEWTON METHOD............................................................................. 3.7 NEWTON’S METHOD FOR NONLINEAR SYSTEMS............................................................................................... APPLIED PROBLEMS................................................................................... 41 42 50 57 62 72 74 80 86 vii
Contents viii 4 System of Linear Equations 93 4.1 MATRICES AND MATRIX OPERATIONS..................................... 94 4.2 NAIVE GAUSSIAN ELIMINATION................................................. 97 4.3 GAUSSIAN ELIMINATION WITH SCALED PARTIAL PIVOTING............................................................................. 105 4.4 LU DECOMPOSITION .......................................................................... 118 4.4.1 Crout’s and Cholesky’s methods................................................. 119 4.4.2 Gaussian elimination method .................................................... 122 4.5 ITERATIVE METHODS.......................................................................... 132 4.5.1 Jacobi iterative method.................................................................132 4.5.2 Gauss-Seidel iterative method.................................................... 134 4.5.3 Convergence................................................................... 137 APPLIED PROBLEMS...................................................................................... 145 5 Interpolation 153 5.1 POLYNOMIAL INTERPOLATION THEORY..................................... 154 5.2 NEWTON’S DIVIDED-DIFFERENCE INTERPOLATING POLYNOMIAL......................................................................................... 156 5.3 THE ERROR OF THE INTERPOLATING POLYNOMIAL......................................................................................... 167 5.4 LAGRANGE INTERPOLATING POLYNOMIAL........................... .172 APPLIED
PROBLEMS...................................................................................... 177 6 Interpolation with Spline Functions 181 6.1 PIECEWISE LINEAR INTERPOLATION........................................... 182 6.2 QUADRATIC SPLINE............................................................................. 188 6.3 NATURAL CUBIC SPLINES.................................................................192 APPLIED PROBLEMS...................................................................................... 206 7 The 7.1 7.2 7.3 Method of Least-Squares 209 LINEAR LEAST-SQUARES....................................................................210 LEAST-SQUARES POLYNOMIAL....................................................... 216 NONLINEAR LEAST-SQUARES...........................................................224 7.3.1 Exponential form..........................................................................224 7.3.2 Hyperbolic form.............................................................................226 APPLIED PROBLEMS...................................................................................... 232 8 Numerical Optimization 235 8.1 ANALYSIS OF SINGLE-VARIABLE FUNCTIONS............................235 8.2 LINE SEARCH METHODS....................................................................238 8.2.1 Bracketing the minimum..............................................................238 8.2.2 Golden section search....................................................................239 8.2.3 Fibonacci Search
.......................................................................... 241 8.2.4 Parabolic Interpolation.................................................................244 8.3 MINIMIZATION USING DERIVATIVES ........................................... 251
Contents ix 8.3.1 Newton’s method..........................................................................251 8.3.2 Secant method................................................................................252 APPLIED PROBLEMS...................................................................................... 255 9 Numerical Differentiation 257 9.1 NUMERICAL DIFFERENTIATION.................................................... 257 9.2 RICHARDSON’S FORMULA.................................................................264 APPLIED PROBLEMS...................................................................................... 270 10 Numerical Integration 273 10.1 TRAPEZOIDAL RULE ..........................................................................274 10.2 SIMPSON’S RULE................................................................................... 283 10.3 ROMBERG ALGORITHM ....................................................................294 10.4 GAUSSIAN QUADRATURE .................................................................301 APPLIED PROBLEMS...................................................................................... 312 11 Numerical Methods for Linear Integral Equations 317 11.1 INTRODUCTION ................................................................................... 317 11.2 QUADRATURE RULES..........................................................................320 11.2.1 Trapezoidal rule.............................................................................321 11.2.2 The Gauss-Nyström
method....................................................... 323 11.3 THE SUCCESSIVE APPROXIMATIONMETHOD .......................... 330 11.4 SCHMIDT’s METHOD.............................................................................332 11.5 VOLTERRA-TYPE INTEGRAL EQUATIONS..................................334 11.5.1 Euler’s method .............................................................................335 11.5.2 Heun’s method .............................................................................336 APPLIED PROBLEMS...................................................................................... 340 12 Numerical Methods for Differential Equations 343 12.1 EULER’S METHOD................................................................................344 12.2 ERROR ANALYSIS ................................................................................350 12.3 HIGHER-ORDER TAYLOR SERIESMETHODS................................ 355 12.4 RUNGE-KUTTA METHODS.................................................................359 12.5 MULTISTEP METHODS.......................................................................373 12.6 ADAMS-BASHFORTH METHODS....................................................... 374 12.7 PREDICTOR-CORRECTOR METHODS........................................... 383 12.8 ADAMS-MOULTON METHODS.......................................................... 384 12.9 NUMERICAL STABILITY ....................................................................392 12.10 HIGHER-ORDER EQUATIONS AND SYSTEMS OF DIFFERENTIAL
EQUATIONS....................................................... 395 12.11 IMPLICIT METHODS AND STIFF SYSTEMS..................................402 12.12 PHASE PLANE ANALYSIS: CHAOTIC DIFFERENTIAL EQUATIONS............................................................................................ 404 APPLIED PROBLEMS...................................................................................... 410
Contents x 13 Boundary-Value Problems 417 13.1 13.2 FINITE-DIFFERENCE METHODS .................................................... 418 SHOOTING METHODS.......................................................................... 425 13.2.1 The nonlinear case ....................................................................... 425 13.2.2 The linear case ............................................................................. 430 APPLIED PROBLEMS...................................................................................... 437 14 Eigenvalues and Eigenvectors 441 14.1 14.2 14.3 14.4 BASIC THEORY...................................................................................... 441 THE POWER METHOD .......................................................................446 THE QUADRATIC METHOD ..............................................................449 EIGENVALUES FOR BOUNDARY-VALUE PROBLEMS............................................................................................... 458 14.5 BIFURCATIONS IN DIFFERENTIAL EQUATIONS............................................................................................ 461 APPLIED PROBLEMS...................................................................................... 466 15 Dynamical Systems and Chaos 467 . 15.1 A REVIEW OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS............................................................................................ 468 15.2 DEFINITIONS AND THEORETICALCONSIDERATIONS .... 471 15.3 TWO-DIMENSIONAL SYSTEMS ......................... .......................... 478
15.4 CHAOS ..................................................................................................... 490 15.5 LAGRANGIAN DYNAMICS .................................................................495 APPLIED PROBLEMS...................................................................................... 502 16 Partial Differential Equations 505 16.1 PARABOLIC EQUATIONS....................................................................506 16.1.1 Explicit methods ..........................................................................506 16.1.2 Implicit methods ..........................................................................510 16.2 HYPERBOLIC EQUATIONS.................................................................517 16.3 ELLIPTIC EQUATIONS..........................................................................524 16.4 NONLINEAR PARTIAL DIFFERENTIALEQUATIONS..............530 16.4.1 Burger’s equation..........................................................................530 16.4.2 Reaction-diffusion equation...........................................................532 16.4.3 Porous media equation.................................................................533 16.4.4 Hamilton-Jacobi-Bellman equation .......................................... 535 16.5 INTRODUCTION TO FINITE-ELEMENTMETHOD....................... 537 16.5.1 Theory............................................................................................ 538 16.5.2 The Finite-Element Method........................................................544 APPLIED
PROBLEMS...................................................................................... 549 Bibliography and References 551 Appendix 556
Contents xi A Calculus Review A.l A.2 A.3 557 Limits and continuity.................................................................................557 Differentiation............................................................................................. 558 Integration................................................................................................... 558 В MATLAB Built-in Functions 561 C Text MATLAB Functions 565 D MATLAB GUI 567 D.l D.2 D.3 D.4 D.5 D.6 D.7 D.8 D.9 Roots of Equations....................................................................................567 System of Linear Equations .................................................................... 569 Interpolation................................................................................................ 570 The Method of Least Squares................................................................. 570 Integration................................................................................................... 571 Differentiation............................................................................................. 572 Numerical Methods for Differential Equations......................................573 Boundary-Value Problems....................................................................... 573 Numerical Methods for PDEs................................................................. 574 Answers to Selected Exercises 577 Index 611
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| discipline | Mathematik |
| edition | Fourth edition |
| format | Book |
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| id | DE-604.BV045096502 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-01T10:39:27Z |
| institution | BVB |
| isbn | 9781138093072 1138093076 |
| language | English |
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| physical | xv, 615 Seiten Diagramme |
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| spellingShingle | Kharab, Abdelwahab An introduction to numerical methods a MATLAB approach MATLAB (DE-588)4329066-8 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4329066-8 (DE-588)4042805-9 |
| title | An introduction to numerical methods a MATLAB approach |
| title_alt | Numerical methods |
| title_auth | An introduction to numerical methods a MATLAB approach |
| title_exact_search | An introduction to numerical methods a MATLAB approach |
| title_full | An introduction to numerical methods a MATLAB approach Dr. Abdelwahab Kharab (Abu Dhabi University), Professor Ronald B. Guenther (Oregon State University) |
| title_fullStr | An introduction to numerical methods a MATLAB approach Dr. Abdelwahab Kharab (Abu Dhabi University), Professor Ronald B. Guenther (Oregon State University) |
| title_full_unstemmed | An introduction to numerical methods a MATLAB approach Dr. Abdelwahab Kharab (Abu Dhabi University), Professor Ronald B. Guenther (Oregon State University) |
| title_short | An introduction to numerical methods |
| title_sort | an introduction to numerical methods a matlab approach |
| title_sub | a MATLAB approach |
| topic | MATLAB (DE-588)4329066-8 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | MATLAB Numerische Mathematik |
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Inhaltsverzeichnis
THWS Schweinfurt Zentralbibliothek Lesesaal
| Signatur: |
2000 SK 900 K45(4) |
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