Computational partial differential equations using MATLAB:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC Press
2009
|
| Series: | Applied mathematics and nonlinear science
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIII, 364 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 9781420089042 |
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MARC
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| 245 | 1 | 0 | |a Computational partial differential equations using MATLAB |c Jichun Li ; Yi-Tung Chen |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC Press |c 2009 | |
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| 490 | 1 | |a Applied mathematics and nonlinear science |v 17 | |
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Record in the Search Index
| _version_ | 1804138603411931136 |
|---|---|
| adam_text | Contents
Preface
xi
Acknowledgments
xiii
1
Brief Overview of Partial Differential Equations
1
1.1
The paxabolic equations
..................... 1
1.2
The wave equations
........................ 2
1.3
The elliptic equations
...................... 3
1.4
Differential equations in broader areas
............. 3
1.4.1
Electromagnetics
..................... 3
1.4.2
Fluid mechanics
...................... 4
1.4.3
Ground water contamination
.............. 5
1.4.4
Petroleum reservoir simulation
............. 6
1.4.5
Finance modeling
..................... 7
1.4.6
Image processing
..................... 7
1.5
A quick review of numerical methods for PDEs
........ 8
References
10
2
Finite Difference Methods for Parabolic Equations
13
2.1
Introduction
............................ 13
2.2
Theoretical issues: stability, consistence, and convergence
. . 15
2.3
1-D parabolic equations
..................... 16
2.3.1
The ^-method
....................... 16
2.3.2
Some extensions
..................... 19
2.4
2-D and
3-D
parabolic equations
................ 23
2.4.1
Standard explicit and implicit methods
......... 23
2.4.2
The ADI methods for 2-D problems
.......... 25
2.4.3
The ADI methods for
3-D
problems
.......... 28
2.5
Numerical examples with
MATLAB
codes
........... 30
2.6
Bibliographical remarks
..................... 33
2.7
Exercises
.............................. 33
References
36
VI
Computational Partial Differential Equations Using
MATLAB
3
Finite Difference Methods for Hyperbolic Equations
39
3.1
Introduction
............................ 39
3.2
Some basic difference schemes
.................. 40
3.3
Dissipation and dispersion errors
................ 42
3.4
Extensions to conservation laws
................. 44
3.5
The second-order hyperbolic PDEs
............... 45
3.6
Numerical examples with
MATLAB
codes
........... 49
3.7
Bibliographical remarks
..................... 52
3.8
Exercises
.............................. 52
References
54
4
Finite Difference Methods for Elliptic Equations
57
4.1
Introduction
............................ 57
4.2
Numerical solution of linear systems
.............. 59
4.2.1
Direct methods
...................... 59
4.2.2
Simple iterative methods
................. 61
4.2.3
Modern iterative methods
................ 64
4.3
Error analysis with a maximum principle
............ 66
4.4
Some extensions
......................... 68
4.4.1
Mixed boundary conditions
............... 68
4.4.2
Self-adjoint problems
................... 69
4.4.3
A fourth-order scheme
.................. 70
4.5
Numerical examples with
MATLAB
codes
........... 73
4.6
Bibliographical remarks
..................... 75
4.7
Exercises
.............................. 76
References
78
5
High-Order Compact Difference Methods
79
5.1
One-dimensional problems
.................... 79
5.1.1
Spatial discretization
................... 79
5.1.2
Approximations of high-order derivatives
........ 83
5.1.3
Temporal discretization
................. 92
5.1.4
Low-pass spatial filter
.................. 92
5.1.5
Numerical examples with
MATLAB
codes
....... 93
5.2
High-dimensional problems
................... 110
5.2.1
Temporal discretization for 2-D problems
....... 110
5.2.2
Stability analysis
..................... 112
5.2.3
Extensions to
3-D
compact ADI schemes
........ 113
5.2.4
Numerical examples with
MATLAB
codes
....... 114
5.3
Other high-order compact schemes
............... 122
5.3.1
One-dimensional problems
................ 122
5.3.2
Two-dimensional problems
................ 124
5.4
Bibliographical remarks
..................... 127
Table
of Contents
vii
5.5
Exercises
..............................127
References
130
6
Finite Element Methods: Basic Theory
133
6.1
Introduction to one-dimensional problems
...........133
6.1.1
The second-order equation
................133
6.1.2
The fourth-order equation
................136
6.2
Introduction to two-dimensional problems
...........140
6.2.1
The Poisson s equation
..................140
6.2.2
The biharmonic problem
.................142
6.3
Abstract finite element theory
..................143
6.3.1
Existence and uniqueness
................143
6.3.2
Stability and convergence
................145
6.4
Examples of conforming finite element spaces
.........146
6.4.1
Triangular finite elements
................147
6.4.2
Rectangular finite elements
...............149
6.5
Examples of nonconforming finite elements
..........150
6.5.1
Nonconforming triangular elements
...........150
6.5.2
Nonconforming rectangular elements
..........151
6.6
Finite element interpolation theory
...............153
6.6.1
Sobolev spaces
......................154
6.6.2
Interpolation theory
...................155
6.7
Finite element analysis of elliptic problems
...........159
6.7.1
Analysis of conforming finite elements
.........159
6.7.2
Analysis of nonconforming finite elements
.......161
6.8
Finite element analysis of time-dependent problems
......163
6.8.1
Introduction
........................163
6.8.2
FEM
for parabolic equations
..............164
6.9
Bibliographical remarks
.....................167
6.10
Exercises
..............................167
References
169
7
Finite Element Methods: Programming
173
7.1
FEM
mesh generation
......................173
7.2
Forming
FEM
equations
.....................178
7.3
Calculation of element matrices
.................179
7.4
Assembly and implementation of boundary conditions
.... 184
7.5
The
MATLAB
code for
Рг
element
...............185
7.6
The
MATLAB
code for the Qx element
............188
7.7
Bibliographical remarks
.....................193
7.8
Exercises
..............................194
References
197
viii
Computational Partial Differential Equations Using
MATLAB
8
Mixed Finite Element Methods
199
8.1
An abstract formulation
..................... 199
8.2
Mixed methods for elliptic problems
.............. 203
8.2.1
The mixed variational formulation
........... 203
8.2.2
The mixed finite element spaces
............. 205
8.2.3
The error estimates
.................... 208
8.3
Mixed methods for the Stokes problem
............. 211
8.3.1
The mixed variational formulation
........... 211
8.3.2
Mixed finite element spaces
............... 212
8.4
An example
MATLAB
code for the Stokes problem
...... 217
8.5
Mixed methods for viscous incompressible flows
........ 231
8.5.1
The steady Navier-Stokes problem
........... 231
8.5.2
The unsteady Navier-Stokes problem
.......... 233
8.6
Bibliographical remarks
..................... 234
8.7
Exercises
..............................235
References
237
9
Finite Element Methods for Electromagnetics
241
9.1
Introduction to Maxwell s equations
..............241
9.2
The time-domain finite element method
............243
9.2.1
The mixed method
....................243
9.2.2
The standard Galerkin method
.............248
9.2.3
The discontinuous Galerkin method
..........251
9.3
The frequency-domain finite element method
.........256
9.3.1
The standard Galerkin method
.............256
9.3.2
The discontinuous Galerkin method
..........257
9.3.3
The mixed DG method
.................261
9.4
The Maxwell s equations in dispersive media
..........263
9.4.1 Isotropie
cold plasma
...................264
9.4.2
Debye medium
......................268
9.4.3
Lorentz
medium
.....................270
9.4.4
Double-negative metamaterials
.............273
9.5
Bibliographical remarks
.....................281
9.6
Exercises
..............................281
References
283
10
Meshless Methods with Radial Basis Functions
287
10.1
Introduction
............................287
10.2
The radial basis functions
....................288
10.3
The MFS-DRM
..........................291
10.3.1
The fundamental solution of PDEs
...........291
10.3.2
The MFS for Laplace s equation
............294
10.3.3
The MFS-DRM for elliptic equations
..........297
Table
of Contents
ix
10.3.4
Computing particular solutions using RBFs
......300
10.3.5
The RBP-MFS
......................302
10.3.6
The MFS-DRM for the parabolic equations
......302
10.4
Kansa s method
..........................304
10.4.1
Kansa s method for elliptic problems
..........304
10.4.2
Kansa s method for parabolic equations
........305
10.4.3
The Hermite-Birkhoff collocation method
.......306
10.5
Numerical examples with
MATLAB
codes
...........308
10.5.1
Elliptic problems
.....................308
10.5.2
Biharmonic problems
...................315
10.6
Coupling RBF meshless methods with DDM
..........322
10.6.1
Overlapping DDM
....................323
10.6.2
Non-overlapping DDM
..................324
10.6.3
One numerical example
.................325
10.7
Bibliographical remarks
.....................327
10.8
Exercises
..............................328
References
329
11
Other Meshless Methods
335
11.1
Construction of meshless shape functions
............335
11.1.1
The smooth particle hydrodynamics method
......335
11.1.2
The moving least-square approximation
........337
11.1.3
The partition of unity method
..............338
11.2
The element-free Galerkin method
...............340
11.3
The meshless local
Petrov-
Galerkin method
..........342
11.4
Bibliographical remarks
.....................345
11.5
Exercises
..............................345
References
346
Appendix A Answers to Selected Problems
349
Index
361
|
| any_adam_object | 1 |
| author | Li, Jichun |
| author_facet | Li, Jichun |
| author_role | aut |
| author_sort | Li, Jichun |
| author_variant | j l jl |
| building | Verbundindex |
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| callnumber-first | Q - Science |
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| ctrlnum | (OCoLC)227914240 (DE-599)BVBBV035302442 |
| dewey-full | 518/.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518/.64 |
| dewey-search | 518/.64 |
| dewey-sort | 3518 264 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV035302442 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:49Z |
| institution | BVB |
| isbn | 9781420089042 |
| language | English |
| lccn | 2008028119 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017107287 |
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| physical | XIII, 364 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Chapman & Hall/CRC Press |
| record_format | marc |
| series | Applied mathematics and nonlinear science |
| series2 | Applied mathematics and nonlinear science |
| spelling | Li, Jichun Verfasser aut Computational partial differential equations using MATLAB Jichun Li ; Yi-Tung Chen Boca Raton [u.a.] Chapman & Hall/CRC Press 2009 XIII, 364 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Applied mathematics and nonlinear science 17 Includes bibliographical references and index MATLAB Differential equations, Partial Numerical solutions MATLAB (DE-588)4329066-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Computermathematik (DE-588)4788218-9 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Numerisches Verfahren (DE-588)4128130-5 s MATLAB (DE-588)4329066-8 s DE-604 Differentialgleichung (DE-588)4012249-9 s Computermathematik (DE-588)4788218-9 s 1\p DE-604 Chen, Yi-Tung Sonstige oth Applied mathematics and nonlinear science 17 (DE-604)BV019612358 17 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017107287&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Li, Jichun Computational partial differential equations using MATLAB Applied mathematics and nonlinear science MATLAB Differential equations, Partial Numerical solutions MATLAB (DE-588)4329066-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Computermathematik (DE-588)4788218-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4329066-8 (DE-588)4128130-5 (DE-588)4012249-9 (DE-588)4788218-9 (DE-588)4044779-0 |
| title | Computational partial differential equations using MATLAB |
| title_auth | Computational partial differential equations using MATLAB |
| title_exact_search | Computational partial differential equations using MATLAB |
| title_full | Computational partial differential equations using MATLAB Jichun Li ; Yi-Tung Chen |
| title_fullStr | Computational partial differential equations using MATLAB Jichun Li ; Yi-Tung Chen |
| title_full_unstemmed | Computational partial differential equations using MATLAB Jichun Li ; Yi-Tung Chen |
| title_short | Computational partial differential equations using MATLAB |
| title_sort | computational partial differential equations using matlab |
| topic | MATLAB Differential equations, Partial Numerical solutions MATLAB (DE-588)4329066-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Computermathematik (DE-588)4788218-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | MATLAB Differential equations, Partial Numerical solutions Numerisches Verfahren Differentialgleichung Computermathematik Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017107287&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019612358 |
| work_keys_str_mv | AT lijichun computationalpartialdifferentialequationsusingmatlab AT chenyitung computationalpartialdifferentialequationsusingmatlab |