Numerical methods based on Sinc and analytic functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
1993
|
| Series: | Springer series in computational mathematics
20 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 533-561 |
| Physical Description: | XV, 565 S. graph. Darst. |
| ISBN: | 0387940081 3540940081 |
Staff View
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| 245 | 1 | 0 | |a Numerical methods based on Sinc and analytic functions |c Frank Stenger |
| 264 | 1 | |a New York u.a. |b Springer |c 1993 | |
| 300 | |a XV, 565 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
Preface v
1 Mathematical Preliminaries 1
1.1 Properties of Analytic Functions 1
Problems for Section 1.1 18
1.2 Hilbert Transforms 22
Problems for Section 1.2 27
1.3 Riemann Hilbert Problems 29
1.3.1 Some Definitions 30
1.3.2 The Index of a Function 31
1.3.3 Homogeneous Problem 35
1.3.4 Solution of the Non Homogeneous Problem 38
Problems for Section 1.3 39
1.4 Fourier Transforms 42
Problems for Section 1.4 52
1.5 Laplace Transforms 55
Problems for Section 1.5 56
1.6 Fourier Series 56
Problems for Section 1.6 62
1.7 Transformations of Functions 65
Problems for Section 1.7 70
1.8 Spaces of Analytic Functions 74
1.8.1 Functions Analytic on the Unit Disc 74
1.8.2 Functions Analytic on fi+ 77
1.8.3 Functions Analytic in the Strip Vd 80
Problems for Section 1.8 84
1.9 The Paley Wiener Theorem 87
Problems for Section 1.9 90
1.10 The Cardinal Function 91
Problems for Section 1.10 97
Historical Remarks on Chapter 1 102
xii Contents
2 Polynomial Approximation 105
2.1 Chebyshev Polynomials 105
Problems for Section 2.1 108
2.2 Discrete Fourier Polynomials 110
Problems for Section 2.2 115
2.3 The Lagrange Polynomial 118
Problems for Section 2.3 122
2.4 Faber Polynomials 127
Problems for Section 2.4 129
Historical Remarks on Chapter 2 130
3 Sine Approximation in Strip 131
3.1 Sine Approximation in T d 131
Problems for Section 3.1 141
3.2 Sine Quadrature on (—oo, oo) 143
Problems for Section 3.2 146
3.3 Discrete Fourier Transforms on (—oo, oo) 147
Problems for Section 3.3 151
3.4 Cauchy Like Transforms on (—00,00) 152
Problems for Section 3.4 160
3.5 Approximation of Derivatives in Vj, 162
Problems for Section 3.5 166
3.6 The Indefinite Integral on (—00,00) 167
Problems for Section 3.6 177
Historical Remarks on Chapter 3 178
4 Sine Approximation on F 179
4.1 Basic Definitions 179
Problems for Section 4.1 182
4.2 Interpolation and Quadrature on F 183
Problems for Section 4.2 197
4.3 Hilbert and Related Transforms on F 201
Problems for Section 4.3 204
4.4 Approximation of Derivatives on F 207
Problems for Section 4.4 217
4.5 Indefinite Integral Over F 218
Problems for Section 4.5 220
4.6 Indefinite Convolution Over F 221
4.6.1 Approximation Procedure 222
4.6.2 Formula Derivation 225
4.6.3 Convergence 228
4.6.4 Applications 234
Problems for Section 4.6 240
Historical Remarks on Chapter 4 240
Contents xiii
5 Sine Related Methods 243
5.1 Introduction 243
5.2 Variations of the Sine Basis 245
Problems for Section 5.2 252
5.3 Elliptic Function Interpolants 252
Problems for Section 5.3 257
5.4 Inversion of the Laplace Transform 258
Problems for Section 5.4 261
5.5 Sine Like Rational Approximation 262
Problems for Section 5.5 276
5.6 Rationals and Extrapolation 276
5.6.1 Pade Approximation 277
5.6.2 Continued Fractions 280
5.6.3 The Epsilon Algorithm and Aitken s A2 Process . . 283
5.6.4 Chebyshev Acceleration 284
5.6.5 Thiele s Algorithm 285
Problems for Section 5.6 291
5.7 Heaviside and Filter Rationals 294
5.7.1 Approximation of the Heaviside Function 295
5.7.2 Approximation of the Filter Function 298
5.7.3 Approximation of the Delta Function 299
Problems for Section 5.7 302
5.8 Positive Base Approximation 304
Problems for Section 5.8 310
Historical Remarks on Chapter 5 310
6 Integral Equations 311
6.1 Introduction 311
6.2 Mathematical Preliminaries 313
6.2.1 Use of Functional Analysis 313
6.2.2 Approximation, Convergence, and Error 317
6.2.3 Fredholm Alternative 320
6.2.4 Perturbed Equations 325
6.2.5 Tikhonov Regularization 326
Problems for Section 6.2 329
6.3 Reduction to Algebraic Equations 331
6.3.1 Galerkin Method 331
6.3.2 Nystrom s Method 331
6.3.3 The Generalized Inverse Procedure 332
6.3.4 Errors in the Numerical Solution 335
Problems for Section 6.3 336
6.4 Volterra Integral Equations 338
6.4.1 Linear Volterra Equations 338
6.4.2 Non Linear Equations via Neumann Series 340
6.4.3 Non Linear Equations by Newton s Method 343
xiv Contents
Problems for Section 6.4 346
6.5 Potential Theory Problems 349
6.5.1 Problem Description 349
6.5.2 Spaces for Sine Approximation 350
6.5.3 Sine Approximation 351
6.5.4 Properties of the Integral Equation 354
6.5.5 Galerkin Approximation 360
6.5.6 Several Surface Patches—Domain Decomposition . . 361
6.5.7 An Explicit Example 364
6.5.8 Kernel Singularities and Integration 374
Problems for Section 6.5 376
6.6 Reduced Wave Equation on a Half Space 379
6.6.1 Problem Description 380
6.6.2 Spaces for Sine Approximation 381
6.6.3 Sine Approximation 383
6.6.4 Properties of the Integral Equation 385
6.6.5 Galerkin Approximation 391
6.6.6 Evaluation of Moment Integrals 392
6.6.7 Numerical Evaluation of Solution 395
6.6.8 An Explicit Example 396
Problems for Section 6.6 398
6.7 Cauchy Singular Integral Equations 400
6.7.1 The Problem 401
6.7.2 The Method of Regularization 401
6.7.3 Properties of the Fredholm Equation 404
6.7.4 Approximation via Nystrom s Method 406
Problems for Section 6.7 407
6.8 Convolution Type Equations 407
6.8.1 The Problems and Theoretical Solutions 407
6.8.2 Approximate Solution 410
6.8.3 Explicit Examples 418
Problems for Section 6.8 421
6.9 The Laplace Transform and Its Inversion 422
Problems for Section 6.9 437
Historical Remarks on Chapter 6 439
7 Differential Equations 441
7.1 ODE IVP 444
7.1.1 Linear Initial Value Problems 445
7.1.2 Non Linear Initial Value Problems 453
Problems for Section 7.1 459
7.2 ODE BVP 465
7.2.1 Sinc Galerkin and Collocation 467
7.2.2 Integration by Parts 469
7.2.3 Collocation and Integration by Parts 470
Contents xv
7.2.4 Convergence of Sinc Galerkin Methods 471
7.2.5 Non Linear Equations 483
7.2.6 Non Homogeneous Boundary Conditions 484
7.2.7 Symmetric Sinc Galerkin Method 486
7.2.8 More Examples 492
Problems for Section 7.2 497
7.3 Analytic Solutions of PDE 500
7.3.1 Analyticity of Solutions in All Variables 501
7.3.2 Analyticity for Sine Approximation 501
7.3.3 Singularities Due to Corners and Edges 506
Problems for Section 7.3 509
7.4 Elliptic Problems 511
Problems for Section 7.4 521
7.5 Hyperbolic Problems 521
Problems for Section 7.5 523
7.6 Parabolic Problems 524
Problems for Section 7.6 529
Historical Remarks on Chapter 7 529
References 533
Index 563
|
| any_adam_object | 1 |
| author | Stenger, Frank |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T17:16:15Z |
| institution | BVB |
| isbn | 0387940081 3540940081 |
| language | English |
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| series | Springer series in computational mathematics |
| series2 | Springer series in computational mathematics |
| spelling | Stenger, Frank Verfasser aut Numerical methods based on Sinc and analytic functions Frank Stenger New York u.a. Springer 1993 XV, 565 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in computational mathematics 20 Literaturverz. S. 533-561 Equations différentielles - Solutions numériques ram Galerkine, méthodes de ram Differential equations Numerical solutions Galerkin methods Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf sinc-Funktion (DE-588)4710623-2 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 gnd rswk-swf Sinc-Methode (DE-588)4325400-7 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Galerkin-Methode (DE-588)4155831-5 gnd rswk-swf Galerkin-Methode (DE-588)4155831-5 s DE-604 Numerisches Verfahren (DE-588)4128130-5 s Analytische Funktion (DE-588)4142348-3 s sinc-Funktion (DE-588)4710623-2 s Numerische Mathematik (DE-588)4042805-9 s Funktionentheorie (DE-588)4018935-1 s Differentialgleichung (DE-588)4012249-9 s Sinc-Methode (DE-588)4325400-7 s Springer series in computational mathematics 20 (DE-604)BV000012004 20 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005413103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stenger, Frank Numerical methods based on Sinc and analytic functions Springer series in computational mathematics Equations différentielles - Solutions numériques ram Galerkine, méthodes de ram Differential equations Numerical solutions Galerkin methods Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd sinc-Funktion (DE-588)4710623-2 gnd Funktionentheorie (DE-588)4018935-1 gnd Analytische Funktion (DE-588)4142348-3 gnd Sinc-Methode (DE-588)4325400-7 gnd Numerische Mathematik (DE-588)4042805-9 gnd Galerkin-Methode (DE-588)4155831-5 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4128130-5 (DE-588)4710623-2 (DE-588)4018935-1 (DE-588)4142348-3 (DE-588)4325400-7 (DE-588)4042805-9 (DE-588)4155831-5 |
| title | Numerical methods based on Sinc and analytic functions |
| title_auth | Numerical methods based on Sinc and analytic functions |
| title_exact_search | Numerical methods based on Sinc and analytic functions |
| title_full | Numerical methods based on Sinc and analytic functions Frank Stenger |
| title_fullStr | Numerical methods based on Sinc and analytic functions Frank Stenger |
| title_full_unstemmed | Numerical methods based on Sinc and analytic functions Frank Stenger |
| title_short | Numerical methods based on Sinc and analytic functions |
| title_sort | numerical methods based on sinc and analytic functions |
| topic | Equations différentielles - Solutions numériques ram Galerkine, méthodes de ram Differential equations Numerical solutions Galerkin methods Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd sinc-Funktion (DE-588)4710623-2 gnd Funktionentheorie (DE-588)4018935-1 gnd Analytische Funktion (DE-588)4142348-3 gnd Sinc-Methode (DE-588)4325400-7 gnd Numerische Mathematik (DE-588)4042805-9 gnd Galerkin-Methode (DE-588)4155831-5 gnd |
| topic_facet | Equations différentielles - Solutions numériques Galerkine, méthodes de Differential equations Numerical solutions Galerkin methods Differentialgleichung Numerisches Verfahren sinc-Funktion Funktionentheorie Analytische Funktion Sinc-Methode Numerische Mathematik Galerkin-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005413103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012004 |
| work_keys_str_mv | AT stengerfrank numericalmethodsbasedonsincandanalyticfunctions |