Partial differential equations with numerical methods:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
[2003]
|
| Series: | Texts in applied mathematics
45 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 259 Seiten Diagramme |
| ISBN: | 3540017720 |
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MARC
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| 245 | 1 | 0 | |a Partial differential equations with numerical methods |c Stig Larsson ; Vidar Thomée |
| 264 | 1 | |a Berlin |b Springer |c [2003] | |
| 264 | 4 | |c © 2003 | |
| 300 | |a IX, 259 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Texts in applied mathematics |v 45 | |
| 650 | 4 | |a Équations aux dérivées partielles - Solutions numériques | |
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Record in the Search Index
| _version_ | 1804129986094825472 |
|---|---|
| adam_text | Table
of
Contents
1
Introduction
.............................................. 1
1.1
Background
............................................ 1
1.2
Notation and Mathematical Preliminaries
.................. 4
1.3
Physical Derivation of the Heat Equation
.................. 7
1.4
Problems
._............................................. 12
2
A Two-Point Boundary Value Problem
................... 15
2.1
The Maximum Principle
................................. 15
2.2
Green s Function
....................................... 18
2.3
Variational Formulation
................................. 20
2.4
Problems
.............................................. 23
3
Elliptic Equations
........................................ 25
3.1
Preliminaries
........................................... 25
3.2
A Maximum Principle
................................... 26
3.3
Dirichlet s Problem for a Disc. Poisson s Integral
........... 28
3.4
Fundamental Solutions. Green s Function
.................. 30
3.5
Variational Formulation of the Dirichlet Problem
........... 32
3.6
A Neumann Problem
................................... 35
3.7
Regularity
............................................. 37
3.8
Problems
.............................................. 38
4
Finite Difference Methods for Elliptic Equations
.......... 43
4.1
A Two-Point Boundary Value Problem
.................... 43
4.2
Poisson s Equation
..................................... 46
4.3
Problems
.............................................. 49
5
Finite Element Methods for Elliptic Equations
............ 51
5.1
A Two-Point Boundary Value Problem
.................... 51
5.2
A Model Problem in the Plane
........................... 57
5.3
Some Facts from Approximation Theory
................... 60
5.4
Error Estimates
........................................ 63
5.5
An A Posteriori Error Estimate
.......................... 66
5.6
Numerical Integration
................................... 67
5.7
A Mixed Finite Element Method
......................... 71
5.8
Problems
.............................................. 73
6
The Elliptic Eigenvalue Problem
.......................... 77
6.1
Eigenfunction Expansions
............................... 77
6.2
Numerical Solution of the Eigenvalue Problem
............. 87
6.3
Problems
.............................................. 93
7
Initial-Value Problems for ODEs
.......................... 95
7.1
The Initial Value Problem for a Linear System
............. 95
7.2
Numerical Solution of ODEs
.............................101
7.3
Problems
..............................................106
8
Parabolic Equations
......................................109
8.1
The Pure Initial Value Problem
..........................109
8.2
Solution by Eigenfunction Expansion
.....................114
8.3
Variational Formulation. Energy Estimates
................120
8.4
A Maximum Principle
...................................122
8.5
Problems
..............................................124
9
Finite Difference Methods for Parabolic Problems
........129
9.1
The Pure Initial Value Problem
..........................129
9.2
The Mixed Initial-Boundary Value Problem
................138
9.3
Problems
..............................................146
10
The Finite Element Method for a Parabolic Problem
.....149
10.1
The
Semidiscrete Galerkin
Finite Element Method
..........149
10.2
Some Completely Discrete Schemes
.......................156
10.3
Problems
..............................................159
11
Hyperbolic Equations
.....................................163
11.1
Characteristic Directions and Surfaces
....................163
11.2
The Wave Equation
.....................................166
11.3
First Order Scalar Equations
.............................169
11.4
Symmetric Hyperbolic Systems
...........................173
11.5
Problems
..............................................181
12
Finite Difference Methods for Hyperbolic Equations
......185
12.1
First Order Scalar Equations
.............................185
12.2
Symmetric Hyperbolic Systems
...........................192
12.3
The Wendroff Box Scheme
...............................196
12.4
Problems
..............................................198
13
The Finite Element Method for Hyperbolic Equations
___201
13.1
The Wave Equation
.....................................201
13.2
First Order Hyperbolic Equations
........................205
13.3
Problems
...... ........................................216
14
Some Other Classes of Numerical Methods
...............217
14.1
Collocation Methods
....................................217
14.2
Spectral Methods
.......................................218
14.3
Finite Volume Methods
.................................219
14.4
Boundary Element Methods
.............................221
14.5
Problems
..............................................223
A Some Tools from Mathematical Analysis
..................225
A.I Abstract Linear Spaces
..................................225
A.2 Function Spaces
........................................231
A.3 The Fourier Transform
..................................238
A.4 Problems
..............................................240
В
Orientation on Numerical Linear Algebra
.................245
B.I Direct Methods
........................................245
B.2 Iterative Methods. Relaxation, Overrelaxation, and
Acceleration
...........................................246
B.3 Alternating Direction Methods
...........................248
B.4 Preconditioned Conjugate Gradient Methods
...............249
B.5 Multigrid and Domain Decomposition Methods
............250
Bibliography
..................................................253
Index
.........................................................257
|
| any_adam_object | 1 |
| author | Larsson, Stig 1952- Thomée, Vidar 1933- |
| author_GND | (DE-588)129915505 (DE-588)108383547 |
| author_facet | Larsson, Stig 1952- Thomée, Vidar 1933- |
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| dewey-full | 515/.353 515/.35321 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 515/.353 21 |
| dewey-search | 515/.353 515/.353 21 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017111811 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:13:51Z |
| institution | BVB |
| isbn | 3540017720 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010317811 |
| oclc_num | 52152408 |
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| physical | IX, 259 Seiten Diagramme |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Larsson, Stig 1952- Verfasser (DE-588)129915505 aut Partial differential equations with numerical methods Stig Larsson ; Vidar Thomée Berlin Springer [2003] © 2003 IX, 259 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 45 Équations aux dérivées partielles - Solutions numériques Differential equations, Partial -- Numerical solutions Numerisches Verfahren (DE-588)4128130-5 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 DE-604 Thomée, Vidar 1933- Verfasser (DE-588)108383547 aut Texts in applied mathematics 45 (DE-604)BV002476038 45 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010317811&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Larsson, Stig 1952- Thomée, Vidar 1933- Partial differential equations with numerical methods Texts in applied mathematics Équations aux dérivées partielles - Solutions numériques Differential equations, Partial -- Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4044779-0 |
| title | Partial differential equations with numerical methods |
| title_auth | Partial differential equations with numerical methods |
| title_exact_search | Partial differential equations with numerical methods |
| title_full | Partial differential equations with numerical methods Stig Larsson ; Vidar Thomée |
| title_fullStr | Partial differential equations with numerical methods Stig Larsson ; Vidar Thomée |
| title_full_unstemmed | Partial differential equations with numerical methods Stig Larsson ; Vidar Thomée |
| title_short | Partial differential equations with numerical methods |
| title_sort | partial differential equations with numerical methods |
| topic | Équations aux dérivées partielles - Solutions numériques Differential equations, Partial -- Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Équations aux dérivées partielles - Solutions numériques Differential equations, Partial -- Numerical solutions Numerisches Verfahren Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010317811&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT larssonstig partialdifferentialequationswithnumericalmethods AT thomeevidar partialdifferentialequationswithnumericalmethods |