Numerical solution of partial differential equations: finite difference methods
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1978
|
| Ausgabe: | second edition |
| Schriftenreihe: | Oxford applied mathematics and computing science series.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 304 Seiten Diagramme |
| ISBN: | 0198596251 019859626X |
Internformat
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| 100 | 1 | |a Smith, Gordon D. |0 (DE-588)1158286333 |4 aut | |
| 245 | 1 | 0 | |a Numerical solution of partial differential equations |b finite difference methods |c G. D. Smith ; Brunel University |
| 250 | |a second edition | ||
| 264 | 1 | |a Oxford |b Clarendon Press |c 1978 | |
| 300 | |a xii, 304 Seiten |b Diagramme | ||
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| 650 | 7 | |a Équations aux dérivées partielles |2 ram | |
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| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
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Datensatz im Suchindex
| _version_ | 1804117638910050304 |
|---|---|
| adam_text | Contents
1. INTRODUCTION AND FINITE DIFFERENCE
FORMULAE 1
Descriptive treatment of elliptic equations 1
Descriptive treatment of parabolic and hyperbolic equations 4
Finite difference approximations to derivatives 6
Notation for functions of several variables 7
2. PARABOLIC EQUATIONS 11
Transformation to non dimensional form 11
An explicit finite difference approximation to dn/dt = d2uldx2 12
A worked example covering three cases and including compari¬
son tables 14
Crank Nicolson implicit method 18
Worked example including a comparison table 21
Solution of the implicit equations by Gauss s elimination method 23
The stability of the elimination method 26
A weighted average approximation 27
Derivative boundary conditions 28
Worked examples including comparison tables:
(i) Explicit formula and central differenced boundary condi¬
tion 30
(ii) Explicit formula and forward differenced boundary condi¬
tion 33
(iii) Implicit formula and central differenced boundary condi¬
tion 35
Alternating direction implicit method 37
Finite difference approximations to du/dt = V2w in cylindrical and
spherical polar co ordinates 40
lair
A worked example involving Km 42
x *O X OX
Miscellaneous methods for improving accuracy: 44
(i) Reduction of the local truncation error—the Douglas
equations ^4
(ii) Use of three time level difference equations 45
(iii) Deferred correction method 46
(iv) Richardson s deferred approach to the limit 48
xii Contents
Deferred approach to the limit, (iii) Deferred correction
method, (iv) More accurate finite difference formulae including
the nine point formula 217
Analysis of the discretization error of the five point approxima¬
tion to Poisson s equation over a rectangle. Quoted result for
irregular boundaries 220
Comments on the solution of difference equations, covering
Gauss elimination, LU decomposition, rounding errors, ill
conditioning, iterative refinement, iterative methods 224
Systematic iterative methods for large linear systems 227
Jacobi, Gauss Seidel and SOR methods 228
A worked example covering each method 231
Jacobi, Gauss Seidel and SOR methods in matrix form 234
A necessary and sufficient condition for convergence of iterative
methods 236
A sufficient condition for convergence 237
Asymptotic and average rates of convergence 239
Methods for accelerating convergence, (i) Lyusternik s method.
(ii) Aitken s method. An illustrative example 239
The optimum accelerating parameter for the SOR method.
Necessary theorems 243
Proof of (A + a) — I)2 = A b2|u,2 for block tridiagonal coefficient
matrices 245
The special case = 1 248
Proof of Bb = 2/[l + V{1 P2(B)}] 250
The calculation of ob for a rectangle and other solution domains 252
Re ordering of equations and unknowns 252
Point iterative methods and re orderings 254
Introduction to 2 cyclic matrices and consistent ordering 255
2 cyclic matrices 255
Ordering vectors for 2 cyclic matrices 257
Consistent ordering of a 2 cyclic matrix 258
The ordering vector for a block tridiagonal matrix 260
An example of a consistently ordered 2 cyclic matrix that is not
block tridiagonal 263
Additional comments on consistent ordering and the SOR
method 263
Consistent orderings associated with the five point approximation
to Poisson s equation 264
Stone s strongly implicit iterative method 268
Two recent direct methods: 274
(i) A method for variables separable equations 274
(ii) George s dissection method 277
Exercises and solutions 277
INDEX 301
|
| any_adam_object | 1 |
| author | Smith, Gordon D. |
| author_GND | (DE-588)1158286333 |
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| bvnumber | BV003290649 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | second edition |
| format | Book |
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| id | DE-604.BV003290649 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:57:35Z |
| institution | BVB |
| isbn | 0198596251 019859626X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002074204 |
| oclc_num | 3915448 |
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| physical | xii, 304 Seiten Diagramme |
| publishDate | 1978 |
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| publisher | Clarendon Press |
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| series2 | Oxford applied mathematics and computing science series. |
| spelling | Smith, Gordon D. (DE-588)1158286333 aut Numerical solution of partial differential equations finite difference methods G. D. Smith ; Brunel University second edition Oxford Clarendon Press 1978 xii, 304 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Oxford applied mathematics and computing science series. Équations aux dérivées partielles ram Difference equations Numerical solutions Differential equations, Partial Numerical solutions Finite-Differenzen-Methode (DE-588)4194626-1 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differenzenverfahren (DE-588)4134362-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Differenzengleichung (DE-588)4012264-5 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Numerisches Verfahren (DE-588)4128130-5 s Differenzenverfahren (DE-588)4134362-1 s 1\p DE-604 Finite-Differenzen-Methode (DE-588)4194626-1 s 2\p DE-604 Numerische Mathematik (DE-588)4042805-9 s 3\p DE-604 Differenzengleichung (DE-588)4012264-5 s 4\p DE-604 Differentialgleichung (DE-588)4012249-9 s 5\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002074204&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Smith, Gordon D. Numerical solution of partial differential equations finite difference methods Équations aux dérivées partielles ram Difference equations Numerical solutions Differential equations, Partial Numerical solutions Finite-Differenzen-Methode (DE-588)4194626-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Differenzenverfahren (DE-588)4134362-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Differenzengleichung (DE-588)4012264-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4194626-1 (DE-588)4128130-5 (DE-588)4012249-9 (DE-588)4134362-1 (DE-588)4044779-0 (DE-588)4012264-5 (DE-588)4042805-9 |
| title | Numerical solution of partial differential equations finite difference methods |
| title_auth | Numerical solution of partial differential equations finite difference methods |
| title_exact_search | Numerical solution of partial differential equations finite difference methods |
| title_full | Numerical solution of partial differential equations finite difference methods G. D. Smith ; Brunel University |
| title_fullStr | Numerical solution of partial differential equations finite difference methods G. D. Smith ; Brunel University |
| title_full_unstemmed | Numerical solution of partial differential equations finite difference methods G. D. Smith ; Brunel University |
| title_short | Numerical solution of partial differential equations |
| title_sort | numerical solution of partial differential equations finite difference methods |
| title_sub | finite difference methods |
| topic | Équations aux dérivées partielles ram Difference equations Numerical solutions Differential equations, Partial Numerical solutions Finite-Differenzen-Methode (DE-588)4194626-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Differenzenverfahren (DE-588)4134362-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Differenzengleichung (DE-588)4012264-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Équations aux dérivées partielles Difference equations Numerical solutions Differential equations, Partial Numerical solutions Finite-Differenzen-Methode Numerisches Verfahren Differentialgleichung Differenzenverfahren Partielle Differentialgleichung Differenzengleichung Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002074204&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT smithgordond numericalsolutionofpartialdifferentialequationsfinitedifferencemethods |