Block method for solving the Laplace equation and for constructing conformal mappings:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton u.a.
CRC Press
1994
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 227 S. graph. Darst. |
| ISBN: | 0849394066 |
Internformat
MARC
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| 100 | 1 | |a Volkov, Evgenij A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Block method for solving the Laplace equation and for constructing conformal mappings |c E. A. Volkov |
| 264 | 1 | |a Boca Raton u.a. |b CRC Press |c 1994 | |
| 300 | |a X, 227 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Applications conformes |2 ram | |
| 650 | 7 | |a Fonctions harmoniques |2 ram | |
| 650 | 4 | |a Conformal mapping | |
| 650 | 4 | |a Harmonic functions | |
| 650 | 0 | 7 | |a Harmonische Funktion |0 (DE-588)4159122-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Approximationstheorie |0 (DE-588)4120913-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Konforme Abbildung |0 (DE-588)4164968-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Laplace-Gleichung |0 (DE-588)4228341-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Laplace-Gleichung |0 (DE-588)4228341-3 |D s |
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| 689 | 0 | 3 | |a Approximationstheorie |0 (DE-588)4120913-8 |D s |
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Datensatz im Suchindex
| _version_ | 1804124245565898752 |
|---|---|
| adam_text | IMAGE 1
E.H. VOLHOV
SOLVING THE
LAPLACE EQUATION AND FOR CONSTRUCTING CONFORMAL IFLAPPINGS
CRC PRESS BOCA RATON ANN ARBOR LONDON TOKYO
IMAGE 2
VII
CONTENTS
C H A P T ER 1. A P P R O X I M A TE B L O CK M E T H OD FOR S O L V I
NG T HE
LAPLACE E Q U A T I ON ON P O L Y G O NS 1
1. SETTING UP A MIXED BOUNDARY-VALUE PROBLEM FOR THE LAPLACE EQUATION ON
A POLYGON 1
1.1. DESCRIPTION OF THE BOUNDARY OF A POLYGON 1
1.2. SETTING UP A BOUNDARY-VALUE PROBLEM 7
2. A FINITE COVERING OF A POLYGON BY BLOCKS OF THREE
TYPES 13
3. REPRESENTATION OF THE SOLUTION OF A BOUNDARY-VALUE PROBLEM ON BLOCKS
19
3.1. CARRIER FUNCTIONS 19
3.2. PRELIMINARY LEMMAS 24
3.3. REPRESENTATION OF THE SOLUTION ON BLOCKS 30
3.4. ADDITIONAL LEMMAS 32
4. AN ALGEBRAIC PROBLEM 34
5. THE MAIN RESULT 40
5.1. THEOREM ON THE CONVERGENCE OF THE BLOCK METHOD 40
5.2. DISCUSSION OF THE THEOREM 42
6. PROOFS OF THEOREM 5.1 AND OF LEMMAS 4.1-4.4 48
6.1. PRELIMINARY LEMMAS 48
6.2. THEOREM ON THE SOLVABILITY OF AN ALGEBRAIC PROBLEM 54
6.3. FUNDAMENTAL LEMMAS 58
IMAGE 3
VUEI CONTENTS
6.4. PROOF OF THEOREM 5.1 66
6.5. PROOFS OF LEMMAS 4.2-4.4 67
7. THE STABILITY AND THE LABOR CONTENT OF COMPUTATIONS REQUIRED BY THE
BLOCK METHOD 73
7.1. PRELIMINARY LEMMAS 73
7.2. VERIFICATION OF THE CRITERION OF SOLVABILITY OF AN ALGEBRAIC
PROBLEM 77
7.3. THE STABILITY OF THE BLOCK METHOD IN A UNIFORM METRIE 79
7.4. THE LABOR OF COMPUTATIONS REQUIRED BY THE BLOCK METHOD 83
8. APPROXIMATION OF A CONJUGATE HARMONIE FUNCTION ON BLOCKS 85
9. NEUMANN S PROBLEM 92
9.1. THE SOLVABILITY OF NEUMANN S PROBLEM ON A POLYGON 92
9.2. APPROXIMATE SOLVING OF NEUMANN S PROBLEM BY BLOCK METHOD 96
10. THE CASE OF ARBITRARY ANALYTIC MIXED BOUNDARY CONDITIONS 98
CHAPTER 2. APPROXIMATE BLOCK METHOD OF CONFORMAL MAPPING OF POLYGONS
ONTO CANONICAL DOMAINS . . .. 108
11. APPROXIMATE CONFORMAL MAPPING OF A SIMPLY- CONNECTED POLYGON ONTO A
DISK 108
12. BASIC HARMONIE FUNCTIONS 111
13. APPROXIMATE CONFORMAL MAPPING OF A MULTIPLYCONNECTED POLYGON ONTO A
PLANE WITH CUTS ALONG PARALLEL LINE SEGMENTS 113
13.1. STRUCTURE OF A MAPPING 113
13.2. CONSTRUCTING AN APPROXIMATE MAPPING 115
14. APPROXIMATE CONFORMAL MAPPING OF A MULTIPLYCONNECTED POLYGON ONTO A
RING WITH CUTS ALONG THE ARES OF CONCENTRIC CIRCLES 119
14.1. STRUCTURE OF A MAPPING 119
14.2. CONSTRUCTING AN APPROXIMATE MAPPING 122
IMAGE 4
CONTENTS IX
C H A P T ER 3. D E V E L O P M E NT A ND A P P L I C A T I ON OF T HE
A P P R O X I M A TE B L O CK M E T H OD FOR C O N F O R M AL M A P P I
NG OF S I M P L Y - C O N N E C T ED A ND D O U B L Y - C O N N E C T ED
D O M A I NS 124
15. APPROXIMATE CONFORMAL MAPPING OF SOME POLYGONS ONTO A STRIP 124
15.1. SCHEME OF CONSTRUCTING A MAPPING 124
15.2. MAPPING OF A RECTANGLE 125
15.3. MAPPING OF TWO OCTAGONS ONTO A STRIP AND OF A
T-SHAPED DOMAIN ONTO A HALF-STRIP 133
16. SCHEME OF CONSTRUCTING A CONFORMAL MAPPING OF A DOUBLY-CONNECTED
DOMAIN ONTO A RING 141
17. MAPPING A SQUARE FRAME ONTO A RING 143
18. MAPPING A SQUARE WITH A CIRCULAR HOLE USING CIRCULAR LUNE BLOCK 149
19. REPRESENTATION OF A HARMONIE FUNCTION ON A RING . . . 155
20. USING A BLOCK-RING FOR MAPPING DOMAIN (18.1) ONTO A RING 157
21. A BLOCK-BRIDGE 161
22. LIMIT CASES 167
23. MAPPING A DISK WITH AN ELLIPTIC HOLE OR WITH A
RETROSECTION ONTO A RING 169
24. MAPPING A DISK WITH A REGULAER POLYGONAL HOLE 173
25. MAPPING THE EXTERIOR OF A PARABOLA WITH A HOLE ONTO A
RING 181
C H A P T ER 4. A P P R O X I M A TE C O N F O R M AL M A P P I NG OF D
O M A I NS W I TH A P E R I O D IC S T R U C T U RE BY T HE B L O CK
M E T H OD 188
26. MAPPING A DOMAIN OF THE TYPE OF HALF-PLANE WITH A
PERIODIC STRUCTURE ONTO A HALF-PLANE 188
26.1. CONSTRUCTION OF A CONFORMAL MAPPING OF A DOMAIN OF THE TYPE OF
HALF-PLANE WITH A PERIODIC BOUNDARY ONTO A HALF-PLANE 188
26.2. CONSTRUCTING BLOCKS 191
26.3. THE ALGORITHM 194
IMAGE 5
X CONTENTS
26.4. PRACTICAL RESULTS 196
26.5. T HE GENERAL CASE 198
27. MAPPING A DOMAIN OF THE TYPE OF STRIP WITH A PERIODIC STRUCTURE ONTO
A STRIP 202
27.1. CONTRUCTION OF A CONFORMAL MAPPING OF A DOMAIN OF THE TYPE OF
STRIP WITH A PERIODIC BOUNDARY
ONTO A STRIP 202
27.2. CONSTRUCTING BLOCKS 203
27.3. THE ALGORITHM 205
27.4. PRACTICAL RESULTS 207
27.5. T HE GENERAL CASE 208
28. MAPPING THE EXTERIOR OF A LATTICE OF ELLIPSES ONTO THE
EXTERIOR OF A LATTICE OF PLATES 210
28.1. SCHEME OF MAPPING 210
28.2. CONSTRUCTING BLOCKS 211
28.3. THE ALGORITHM 213
28.4. PRACTICAL RESULTS 216
R E F E R E N C ES 220
I N D EX 225
|
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| author | Volkov, Evgenij A. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:42:36Z |
| institution | BVB |
| isbn | 0849394066 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006546855 |
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| physical | X, 227 S. graph. Darst. |
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| publisher | CRC Press |
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| spelling | Volkov, Evgenij A. Verfasser aut Block method for solving the Laplace equation and for constructing conformal mappings E. A. Volkov Boca Raton u.a. CRC Press 1994 X, 227 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applications conformes ram Fonctions harmoniques ram Conformal mapping Harmonic functions Harmonische Funktion (DE-588)4159122-7 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Konforme Abbildung (DE-588)4164968-0 gnd rswk-swf Laplace-Gleichung (DE-588)4228341-3 gnd rswk-swf Laplace-Gleichung (DE-588)4228341-3 s Harmonische Funktion (DE-588)4159122-7 s Konforme Abbildung (DE-588)4164968-0 s Approximationstheorie (DE-588)4120913-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006546855&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Volkov, Evgenij A. Block method for solving the Laplace equation and for constructing conformal mappings Applications conformes ram Fonctions harmoniques ram Conformal mapping Harmonic functions Harmonische Funktion (DE-588)4159122-7 gnd Approximationstheorie (DE-588)4120913-8 gnd Konforme Abbildung (DE-588)4164968-0 gnd Laplace-Gleichung (DE-588)4228341-3 gnd |
| subject_GND | (DE-588)4159122-7 (DE-588)4120913-8 (DE-588)4164968-0 (DE-588)4228341-3 |
| title | Block method for solving the Laplace equation and for constructing conformal mappings |
| title_auth | Block method for solving the Laplace equation and for constructing conformal mappings |
| title_exact_search | Block method for solving the Laplace equation and for constructing conformal mappings |
| title_full | Block method for solving the Laplace equation and for constructing conformal mappings E. A. Volkov |
| title_fullStr | Block method for solving the Laplace equation and for constructing conformal mappings E. A. Volkov |
| title_full_unstemmed | Block method for solving the Laplace equation and for constructing conformal mappings E. A. Volkov |
| title_short | Block method for solving the Laplace equation and for constructing conformal mappings |
| title_sort | block method for solving the laplace equation and for constructing conformal mappings |
| topic | Applications conformes ram Fonctions harmoniques ram Conformal mapping Harmonic functions Harmonische Funktion (DE-588)4159122-7 gnd Approximationstheorie (DE-588)4120913-8 gnd Konforme Abbildung (DE-588)4164968-0 gnd Laplace-Gleichung (DE-588)4228341-3 gnd |
| topic_facet | Applications conformes Fonctions harmoniques Conformal mapping Harmonic functions Harmonische Funktion Approximationstheorie Konforme Abbildung Laplace-Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006546855&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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