Numerical methods for grid equations: 1 Direct methods
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1989
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXXV, 242 S. |
| ISBN: | 3764322764 0817622764 |
Internformat
MARC
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| 100 | 1 | |a Samarskij, Aleksandr A. |d 1919- |e Verfasser |0 (DE-588)107587351 |4 aut | |
| 240 | 1 | 0 | |a Metody rešenija setočnych uravnenij |
| 245 | 1 | 0 | |a Numerical methods for grid equations |n 1 |p Direct methods |c Aleksandr A. Samarskii ; Evgenii S. Nikolaev |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1989 | |
| 300 | |a XXXV, 242 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 700 | 1 | |a Nikolaev, Evgenij S. |e Verfasser |4 aut | |
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| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001196411&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804116267827724288 |
|---|---|
| adam_text | Volume I
Table of Contents
Volume II: Table of Contents ix
Preface xvii
Introduction xxi
Chapter 1
Direct Methods for Solving Difference Equations 1
1.1 Grid equations. Basic concepts 1
1.1.1 Grids and grid functions 1
1.1.2 Difference derivatives and various difference identities 4
1.1.3 Grid and difference equations 8
1.1.4 The Cauchy problem and boundary value
problems for difference equations 13
1.2 The general theory of linear difference equations 17
1.2.1 Properties of the solutions of homogeneous equations 17
1.2.2 Theorems about the solutions of linear equations 20
1.2.3 The method of variation of parameters 21
1.2.4 Examples 26
1.3 The solution of linear equations with constant coefficients 30
1.3.1 The characteristic equation. The simple roots case 30
1.3.2 The multiple root case 31
1.3.3 Examples 35
1.4 Second order equations with constant coefficients 38
1.4.1 The general solution of a homogeneous equation 38
1.4.2 The Chebyshev polynomials 41
1.4.3 The general solution of a non homogeneous equation 44
vi Volume I: Table of Contents
1.5 Eigenvalue difference problems 48
1.5.1 A boundary value problem of the first kind 48
1.5.2 A boundary value problem of the second kind 50
1.5.3 A mixed boundary value problem 52
1.5.4 A periodic boundary value problem 54
Chapter 2
The Elimination Method 61
2.1 The elimination method for three point equations 61
2.1.1 The algorithm 61
2.1.2 Two sided elimination 65
2.1.3 Justification of the elimination method 66
2.1.4 Sample applications of the elimination method 70
2.2 Variants of the elimination method 73
2.2.1 The flow variant of the elimination method 73
2.2.2 The cyclic elimination metod 77
2.2.3 The elimination method for complicated systems 81
2.2.4 The non monotonic elimination method 86
2.3 The elimination method for five point equations 90
2.3.1 The monotone elimination algorithm 90
2.3.2 Justification of the method 92
2.3.3 A variant of non monotonic elimination 95
2.4 The block elimination method 97
2.4.1 Systems of vector equations 97
2.4.2 Elimination for three point vector equations 101
2.4.3 Elimination for two point vector equations 104
2.4.4 Orthogonal elimination for two point vector equations .... 107
2.4.5 Elimination for three point equations
with constant coefficents 112
Chapter 3
The Cyclic Reduction Method 117
3.1 Boundary value problems for three point vector equations 117
3.1.1 Statement of the boundary value problems 117
3.1.2 A boundary value problem of the first kind 119
3.1.3 Other boundary value problems for difference equations ... 122
3.1.4 A high accuracy Dirichlet difference problem 126
3.2 The cylic reduction method for a
boundary value problem of the first kind 128
3.2.1 The odd even elimination process 128
Volume I: Table of Contents vii
3.2.2 Transformation of the right hand
side and inversion of the matrices 131
3.2.3 The algorithm for the method 136
3.2.4 The second algorithm of the method 139
3.3 Sample applications of the method 145
3.3.1 A Dirichlet difference problem for
Poisson s equation in a rectangle 145
3.3.2 A high accuracy Dirichlet difference problem 148
3.4 The cyclic reduction method for other boundary value problems . 151
3.4.1 A boundary value problem of the second kind 151
3.4.2 A periodic problem 157
3.4.3 A boundary value problem of the third kind 161
Chapter 4
The Separation of Variables Method 171
4.1 The algorithm for the discrete Fourier transform 171
4.1.1 Statement of the problem 171
4.1.2 Expansion in sines and shifted sines 176
4.1.3 Expansion in cosines 185
4.1.4 Transforming a real valued periodic grid function 188
4.1.5 Transforming a complex valued periodic grid function 193
4.2 The solution of difference problems by the Fourier method 196
4.2.1 Eigenvalue difference problems for
the Laplace operator in a rectangle 196
4.2.2 Poisson s equation in a rectangle;
expansion in a double series 201
4.2.3 Expansion in a single series 205
4.3 The method of incomplete reduction 211
4.3.1 Combining the Fourier and reduction methods 211
4.3.2 The solution of boundary value problems
for Poisson s equation in a rectangle 219
4.3.3 A high accuracy Dirichlet
difference problem in a rectangle 223
4.4 The staircase algorithm and the reduction method
for solving tridiagonal systems of equations 227
4.4.1 The staircase algorithm for the case of
tridiagonal matrices with scalar elements 227
4.4.2 The staircase algorithm for the
case of a block tridiagonal matrix 230
4.4.3 Stability of the staircase algorithm 231
4.4.4 The reduction method for three point scalar equations .... 236
Index 239
|
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| author | Samarskij, Aleksandr A. 1919- Nikolaev, Evgenij S. |
| author_GND | (DE-588)107587351 |
| author_facet | Samarskij, Aleksandr A. 1919- Nikolaev, Evgenij S. |
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| author_sort | Samarskij, Aleksandr A. 1919- |
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| id | DE-604.BV001775255 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:35:48Z |
| institution | BVB |
| isbn | 3764322764 0817622764 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001196411 |
| oclc_num | 180494176 |
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| owner_facet | DE-12 DE-91 DE-BY-TUM DE-384 DE-703 DE-739 DE-824 DE-706 DE-634 DE-188 DE-11 DE-83 |
| physical | XXXV, 242 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Samarskij, Aleksandr A. 1919- Verfasser (DE-588)107587351 aut Metody rešenija setočnych uravnenij Numerical methods for grid equations 1 Direct methods Aleksandr A. Samarskii ; Evgenii S. Nikolaev Basel [u.a.] Birkhäuser 1989 XXXV, 242 S. txt rdacontent n rdamedia nc rdacarrier Nikolaev, Evgenij S. Verfasser aut (DE-604)BV001775254 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001196411&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Samarskij, Aleksandr A. 1919- Nikolaev, Evgenij S. Numerical methods for grid equations |
| title | Numerical methods for grid equations |
| title_alt | Metody rešenija setočnych uravnenij |
| title_auth | Numerical methods for grid equations |
| title_exact_search | Numerical methods for grid equations |
| title_full | Numerical methods for grid equations 1 Direct methods Aleksandr A. Samarskii ; Evgenii S. Nikolaev |
| title_fullStr | Numerical methods for grid equations 1 Direct methods Aleksandr A. Samarskii ; Evgenii S. Nikolaev |
| title_full_unstemmed | Numerical methods for grid equations 1 Direct methods Aleksandr A. Samarskii ; Evgenii S. Nikolaev |
| title_short | Numerical methods for grid equations |
| title_sort | numerical methods for grid equations direct methods |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001196411&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001775254 |
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