Handbook of sinc numerical methods:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2011
|
| Series: | Chapman & Hall/CRC numerical analysis and scientific computing
A Chapman & Hall book |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XX, 463 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 9781439821589 1439821585 |
Staff View
MARC
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| 245 | 1 | 0 | |a Handbook of sinc numerical methods |c Frank Stenger |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2011 | |
| 300 | |a XX, 463 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Chapman & Hall/CRC numerical analysis and scientific computing | |
| 490 | 0 | |a A Chapman & Hall book | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Galerkin methods | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
xv
One Dimensional Sine Theory
1
1.1
Introduction and Summary
............... 1
1.1.1
Some Introductory Remarks
........... 2
1.1.2
Uses and Misuses of Sine
............ 5
1.2
Sampling over the Real Line
............... 7
Problems for Section
1.2............. 11
1.3
More General Sine Approximation on
IR
........ 18
1.3.1
Infinite Term Sine Approximation on
IR
.... 18
1.3.2
Finite Term Sine Approximation on
IR
..... 25
Problems for Section
1.3............. 31
1.4
Sine, Wavelets, Trigonometric and Algebraic Polyno¬
mials and Quadratures
.................. 32
1.4.1
A General Theorem
............... 35
1.4.2
Explicit Special Cases on
[0,2
π]
........ 36
1.4.3
Wavelets and Trigonometric Polynomials
... 40
1.4.4
Error of Approximation
............. 42
1.4.5
Algebraic Interpolation and Quadrature
.... 48
1.4.6
Wavelet Differentiation
............. 60
1.4.7
Wavelet Indefinite Integration
.......... 62
1.4.8
Hubert Transforms
................ 63
1.4.9
Discrete Fourier Transform
........... 65
Problems for Section
1.4............. 68
1.5
Sine Methods on
Γ
.................... 70
1.5.1
Sine Approximation on a Finite Interval
.... 70
1.5.2
Sine Spaces for Intervals and Arcs
....... 72
1.5.3
Important Explicit Transformations
...... 79
1.5.4
Interpolation on
Γ
................ 82
ix
1.5.5
Sine Approximation of Derivatives
.......87
1.5.6
Sine Collocation
.................89
1.5.7
Sine Quadrature
.................90
1.5.8
Sine Indefinite Integration
............92
1.5.9
Sine Indefinite Convolution
...........93
1.5.10
Laplace Transform Inversion
..........100
1.5.11
More General
1 —
d
Convolutions
........101
1.5.12
Hubert and Cauchy Transforms
.........105
1.5.13
Analytic Continuation
..............113
1.5.14
Initial Value Problems
..............116
1.5.15 Wiener-Hopf
Equations
.............118
Problems for Section
1.5.............120
1.6
Rational Approximation at Sine Points
.........125
1.6.1
Rational Approximation in
~Μ.α,β,<ΐ{ψ)
.....126
1.6.2
Thiele-Like Algorithms
.............127
Problems for Section
1.6.............128
1.7
Polynomial Methods at Sine Points
...........129
1.7.1
Sine Polynomial Approximation on
(0,1) . . .130
1.7.2
Polynomial Approximation on
Γ
........133
1.7.3
Approximation of the Derivative on
Γ
.....134
Problems for Section
1.7.............137
Sine Convolution-BIE Methods for PDE
&
IE
139
2.1
Introduction and Summary
...............139
2.2
Some Properties of Green s Functions
.........141
2.2.1
Directional Derivatives
..............141
2.2.2
Integrals along Arcs
...............142
2.2.3
Surface Integrals
.................142
2.2.4
Some Green s Identities
.............143
Problems for Section
2.2.............150
2.3
Free-Space Green s Functions for PDE
.........150
2.3.1
Heat Problems
..................151
2.3.2
Wave Problems
..................151
2.3.3
Helmholtz Equations
...............152
2.3.4
Biharmonic Green s Functions
.........154
2.4
Laplace Transforms of Green s Functions
........155
2.4.1
Transforms for
Poisson
Problems
........158
2.4.2
Transforms for Helmholtz Equations
......163
2.4.3
Transforms for Hyperbolic Problems
......168
2.4.4
Wave Equation in
R3 x
(0,T)
.........169
2.4.5
Transforms for Parabolic Problems
.......172
2.4.6
Navier-Stokes Equations
.............173
2.4.7
Transforms for Biharmonic Green s Functions
. 180
Problems for Section
2.4.............184
2.5
Multi-Dimensional Convolution Based on Sine
.... 187
2.5.1
Rectangular Region in
2 —
d
...........187
2.5.2
Rectangular Region in
3 —
d
...........191
2.5.3
Curvilinear Region in
2 -
d
...........192
2.5.4
Curvilinear Region in
3 —
d
...........199
2.5.5
Boundary Integral Convolutions
........207
Problems for Section
2.5.............209
2.6
Theory of Separation of Variables
............209
2.6.1
Regions and Function Spaces
..........210
2.6.2
Analyticity and Separation of Variables
.... 222
Problems for Section
2.6.............242
Explicit
1—
d
Program Solutions via Sine—Pack
243
3.1
Introduction and Summary
...............243
3.2
Sine Interpolation
.....................245
3.2.1
Sine Points Programs
..............246
3.2.2
Sine Basis Programs
...............248
3.2.3
Interpolation and Approximation
........251
3.2.4
Singular, Unbounded Functions
.........257
Problems for Section
3.2.............257
3.3
Approximation of Derivatives
..............258
Problems for Section
3.3.............261
3.4
Sine Quadrature
.....................262
Problems for Section
3.4.............265
3.5
Sine Indefinite Integration
................266
Problems for Section
3.5.............268
3.6
Sine Indefinite Convolution
...............270
Problems for Section
3.6.............274
3.7
Laplace Transform Inversion
...............275
Problems for Section
3.7.............278
3.8
Hubert and Cauchy Transforms
.............280
Problems for Section
3.8.............283
3.9
Sine Solution of ODE
..................284
3.9.1
Nonlinear ODE-IVP on
(0,Г)
via
Picard
... 285
3.9.2
Linear ODE-IVP on
(0,
Γ)
via
Picard
.....286
3.9.3
Linear ODE-IVP on
(0,
T) via Direct Solution
289
3.9.4
Second-Order Equations
.............292
3.9.5 Wiener-Hopf
Equations
.............298
3.10
Wavelet Examples
....................300
3.10.1
Wavelet Approximations
.............302
3.10.2
Wavelet Sol n of a Nonlinear ODE via
Picard
. 309
Explicit Program Solutions of PDE via Sine-Pack
315
4.1
Introduction and Summary
...............315
4.2
Elliptic PDE
.......................315
4.2.1
Harmonic Sine Approximation
.........315
4.2.2
A Poisson-Dirichlet Problem over B2
......320
4.2.3
A Poisson-Dirichlet Problem over a Square
. . 323
4.2.4
Neumann to a Dirichlet Problem on
Lemniscate
....................332
4.2.5
A Poisson
Problem over a Curvilinear Region
in R2
.......................338
4.2.6
A Poisson
Problem over K3
...........350
4.3
Hyperbolic PDE
.....................356
4.3.1
Solving a Wave Equation Over
R3 x
(0,
T)
..356
4.3.2
Solving Helmholtz Equation
...........364
4.4
Parabolic PDE
......................365
4.4.1
A Nonlinear Population Density Problem
. . . 365
4.4.2
Navier-Stokes Example
.............383
4.5
Performance Comparisons
...............404
4.5.1
The Problems
...................404
4.5.2
The Comparisons
.................405
Directory of Programs
409
5.1
Wavelet Formulas
.....................409
5.2
One Dimensional Sine Programs
............410
5.2.1
Standard Sine Transformations
.........410
5.2.2
Sine Points and Weights
.............411
5.2.3
Interpolation at Sine Points
...........412
5.2.4
Derivative Matrices
................413
5.2.5
Quadrature
....................414
5.2.6
Indefinite Integration
...............416
5.2.7
Indefinite Convolution
..............416
5.2.8
Laplace Transform Inversion
..........418
5.2.9
Hubert Transform Programs
..........418
5.2.10
Cauchy Transform Programs
..........419
5.2.11
Analytic Continuation
..............420
5.2.12
Cauchy Transforms
................421
5.2.13
Initial Value Problems
..............421
5.2.14 Wiener-Hopf
Equations
.............422
5.3
Multi-Dimensional Laplace Transform Programs
. . . 422
5.3.1
Q
-
Function Program
..............422
5.3.2
Transf. for
Poisson
Green s Functions
.....422
5.3.3
Transforms of Helmholtz Green s Function
. . . 423
5.3.4
Transforms of Hyperbolic Green s Functions
. . 423
5.3.5
Transforms of Parabolic Green s Functions
. . 424
5.3.6
Transf. of Navier-Stokes Green s Functions
. . 425
5.3.7
Transforms of Biharmonic Green s Functions
. 425
5.3.8
Example Programs for PDE Solutions
.....426
Bibliography
429
Index
461
Mathematics
Handbook of Sine Numerical Methods presents an ideal road map for
handling general numeric problems. Reflecting the author s advances
with Sine since
1995,
the text most notably provides a detailed exposition
of the Sine separation of variables method for numerically solving the
full range of partial differential equations (PDEs) of interest to scientists
and engineers. This new theory, which combines Sine convolution with
the boundary integral equation (IE) approach, makes for exponentially
faster convergence to solutions of differential equations. The basis for
the approach is the Sine method of approximating almost every type of
operation stemming from calculus via easily computed matrices of very
low dimension.
The CD-ROM of this handbook contains roughly
450
MATLAB®
programs
corresponding to exponentially convergent numerical algorithms for
solving nearly every computational problem of science and engineering.
While the book makes Sine methods accessible to users wanting to
bypass the complete theory, it also offers sufficient theoretical details
for readers who do want a full working understanding of this exciting
area of numerical analysis.
Features
»
Develops methods for solving linear and nonlinear PDE problems
with emphasis on elliptic, hyperbolic, and parabolic PDEs
»
Applies
MATLAB
to a range of real-world problems
•
Covers many novel derivations, including Laplace transform
inversion and indefinite convolution
1
Explores advances in nonlinear convolutions and analytic
continuation
1
Offers new insights into properties of PDEs and lEs
Explains the unification of Sine series and Fourier and algebraic
polynomials
Provides a solution to
Wiener-Hopf
problems
Discusses the Sine separation of variables method
ISBN:
47η-1-434η-Ξ15η-4
90000
9 781439 821589
|
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| id | DE-604.BV039559734 |
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| indexdate | 2024-07-10T00:06:16Z |
| institution | BVB |
| isbn | 9781439821589 1439821585 |
| language | English |
| lccn | 2010042046 |
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| owner | DE-703 DE-824 |
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| physical | XX, 463 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2011 |
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| publisher | CRC Press |
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| series2 | Chapman & Hall/CRC numerical analysis and scientific computing A Chapman & Hall book |
| spelling | Stenger, Frank Verfasser aut Handbook of sinc numerical methods Frank Stenger Boca Raton [u.a.] CRC Press 2011 XX, 463 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC numerical analysis and scientific computing A Chapman & Hall book Includes bibliographical references and index Galerkin methods Differential equations Numerical solutions Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411438&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411438&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Stenger, Frank Handbook of sinc numerical methods Galerkin methods Differential equations Numerical solutions |
| title | Handbook of sinc numerical methods |
| title_auth | Handbook of sinc numerical methods |
| title_exact_search | Handbook of sinc numerical methods |
| title_full | Handbook of sinc numerical methods Frank Stenger |
| title_fullStr | Handbook of sinc numerical methods Frank Stenger |
| title_full_unstemmed | Handbook of sinc numerical methods Frank Stenger |
| title_short | Handbook of sinc numerical methods |
| title_sort | handbook of sinc numerical methods |
| topic | Galerkin methods Differential equations Numerical solutions |
| topic_facet | Galerkin methods Differential equations Numerical solutions |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411438&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411438&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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