Partial differential equations with numerical methods:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Edition: | 1. softcover print. |
| Series: | Texts in applied mathematics
45 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 260 S. graph. Darst. |
| ISBN: | 9783540887058 9783540887065 |
Staff View
MARC
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| 245 | 1 | 0 | |a Partial differential equations with numerical methods |c Stig Larsson ; Vidar Thomée |
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| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
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| 490 | 1 | |a Texts in applied mathematics |v 45 | |
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Record in the Search Index
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|---|---|
| adam_text | 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
X Contents
6 The Elliptic Eigenvalue Problem.......................... 77
6.1 Eigenfunction Expansions ............................... 77
6.2 Numerical Solution of the Eigenvalue Problem ............. 88
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.............................I85
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
Contents XI
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
B 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 Thomée, Vidar 1933- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 SK 920 |
| classification_tum | MAT 671f |
| ctrlnum | (OCoLC)298551827 (DE-599)BVBBV035250446 |
| 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 | 3518.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. softcover print. |
| format | Book |
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| id | DE-604.BV035250446 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:29:38Z |
| institution | BVB |
| isbn | 9783540887058 9783540887065 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017056101 |
| oclc_num | 298551827 |
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| owner | DE-20 DE-83 DE-M347 DE-188 DE-703 |
| owner_facet | DE-20 DE-83 DE-M347 DE-188 DE-703 |
| physical | XI, 260 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Larsson, Stig Verfasser aut Partial differential equations with numerical methods Stig Larsson ; Vidar Thomée 1. softcover print. Berlin [u.a.] Springer 2009 XI, 260 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 45 Partielle Differentialgleichung - Numerisches Verfahren 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 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017056101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Larsson, Stig Thomée, Vidar 1933- Partial differential equations with numerical methods Texts in applied mathematics Partielle Differentialgleichung - Numerisches Verfahren 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 | Partielle Differentialgleichung - Numerisches Verfahren Numerisches Verfahren (DE-588)4128130-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Partielle Differentialgleichung - Numerisches Verfahren Numerisches Verfahren Partielle Differentialgleichung |
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