Multidimensional weakly singular integral equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1993
|
| Schriftenreihe: | Lecture notes in mathematics
1549 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 158 S. graph. Darst. |
| ISBN: | 3540568786 0387568786 |
Internformat
MARC
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| 100 | 1 | |a Vainikko, Gennadi |d 1938- |e Verfasser |0 (DE-588)103337075 |4 aut | |
| 245 | 1 | 0 | |a Multidimensional weakly singular integral equations |c Gennadi Vainikko |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1993 | |
| 300 | |a XI, 158 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1549 | |
| 650 | 7 | |a Algorithmee cubature |2 Jussieu | |
| 650 | 7 | |a Analyse numérique |2 Jussieu | |
| 650 | 7 | |a Approximation solution |2 Jussieu | |
| 650 | 7 | |a Collocation |2 Jussieu | |
| 650 | 7 | |a Convergence discrète |2 Jussieu | |
| 650 | 7 | |a Equation intégrale Peierls |2 Jussieu | |
| 650 | 7 | |a Equation intégrale faiblement singulière |2 Jussieu | |
| 650 | 7 | |a Equation intégrale non linéaire |2 Jussieu | |
| 650 | 7 | |a Integraalvergelijkingen |2 gtt | |
| 650 | 7 | |a Interpolation |2 Jussieu | |
| 650 | 7 | |a Transfert radiatif |2 Jussieu | |
| 650 | 4 | |a Équations intégrales - Théorie asymptotique | |
| 650 | 7 | |a Équations intégrales - Théorie asymptotique |2 ram | |
| 650 | 4 | |a Integral equations |x Asymptotic theory | |
| 650 | 0 | 7 | |a Schwache Singularität |0 (DE-588)4180293-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integralgleichung |0 (DE-588)4027229-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diskretisierung |0 (DE-588)4012469-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Asymptotische Methode |0 (DE-588)4287476-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Integralgleichung |0 (DE-588)4027229-1 |D s |
| 689 | 0 | 1 | |a Schwache Singularität |0 (DE-588)4180293-7 |D s |
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| 689 | 1 | 0 | |a Integralgleichung |0 (DE-588)4027229-1 |D s |
| 689 | 1 | 1 | |a Asymptotische Methode |0 (DE-588)4287476-2 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Lecture notes in mathematics |v 1549 |w (DE-604)BV000676446 |9 1549 | |
| 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=005093366&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Datensatz im Suchindex
| _version_ | 1805082754761621504 |
|---|---|
| adam_text |
CONTENTS
1. SOME PROBLEMS LEADING TO MULTIDIMENSIONAL WEAKLY
SINGULAR INTEGRAL EQUATIONS 1
1.1. An interior exterior problem 1
1.2. A physical background (n = 2) 1
1.3. Integral equation formulation (ni3) 2
1.4. Integral equation formulation (n = 2) 3
1.5. Radiation transfer problem 5
1.6. Integral equation formulation of the radiation transfer problem 6
1.7. Peierls integral equations 8
1.8. Exercises 8
2. PRELIMINARIES 10
2.1. Metric dG and space BC(G*) 10
2.2. Weakly singular integral operators 11
2.3. Compactness of a weakly singular integral operator 12
2.4. Weakly singular integral operators with differentiable kernels 16
2.5. Weighted space Cm'v(G) 18
2.6. Weighted space C™ V(G) 21
2.7. Exercises 23
3. SMOOTHNESS OF THE SOLUTION 24
3.1. The class of weakly singular kernels 24
3.2. Main results and comments 27
3.3. Differentiation of weakly singular integral 28
3.4. Estimates of the derivatives of Tu 32
3.5. Proof of Theorem 3.1 35
3.6. Tangential differentiation of weakly singular integral 39
3.7. Estimates of the tangential derivatives of Tu 41
3.8. Proof of Theorem 3.2 42
3.9. Sharpness of Theorem 3.1 (general analysis) 43
3.10. Sharpness of Theorem 3.1 (analysis of model examples) . 47
3.11. Two dimensional integral equation with a logarithmically
singular kernel 49
3.12. Exercises 50
X
4. OUTLINES OF DISCRETE CONVERGENCE THEORY 51
4.1. Discrete convergence and discrete compactness of a family of
elements 51
4.2. Example 52
4.3. Discrete convergence of a family of linear operators 53
4.4. Discrete convergence of approximate solutions 55
4.5. Convergence and convergence rates in eigenvalue problems . . 55
4.6. Approximation of non linear equations 58
4.7. Exercises 59
5. PIECEWISE CONSTANT COLLOCATION AND RELATED METHODS . . 60
5.1. Assumptions about the boundary 60
5.2. Partition of G 63
5.3. PCCM and related methods 65
5.4. Convergence rates of the methods 67
5.5. Block scheme of the proof of Theorem 5.1 69
5.6. Compact convergence of the discretized operators 71
5.7. Approximation error of the basic method 73
5.8. Estimation of prolonged approximate solution 76
5.9. Proof of assertion (ii) 77
5.10. Proof of assertion (iii) 78
5.11. Proof of assertion (iv) 80
5.12. Two grid iteration method 83
5.13. Initial guesses 88
5.14. Amount of arithmetical work 89
5.15. Eigenvalue problem 91
5.16. Exercises 92
6. COMPOSITE CUBATURE ALGORITHMS 94
6.1. Partition of G and composite cubature formulae 94
6.2. Basic methods 96
6.3. Refined cubatures for the evaluation of the coefficients . 97
6.4. Error analysis (preliminaries) 99
6.5. Error analysis of Algorithms 6.1 and 6.2 102
6.6. Error estimates for approximate solution 104
6.7. Some further algorithms 106
6.8. Two grid methods 107
6.9. Case of convolution type integral equations 109
6.10. Exercises 110
XI
7. HIGHER ORDER METHODS 112
7.1. Space C£* V(G) 112
7.2. Piecewise polynomial interpolation 113
7.3. Error estimates of the interpolation 114
7.4. Piecewise polynomial collocation method 121
7.5. Error estimates at the collocation points 124
7.6. Superconvergence at the collocation points 126
7.7. Piecewise constant collocation (m = l) 133
7.8. Piecewise polylinear collocation (m = 2) 134
7.9. Piecewise polysquare collocation (m = 3) 135
7.10. Exercises 136
8. NONLINEAR INTEGRAL EQUATION 137
8.1. Smoothness of the solution 137
8.2. Piecewise constant collocation and related methods 141
8.3. Higher order methods 143
8.4. Exercises 144
BIBLIOGRAPHICAL COMMENTS 145
OPEN PROBLEMS 148
REFERENCES 151
SUBJECT INDEX 159 |
| any_adam_object | 1 |
| author | Vainikko, Gennadi 1938- |
| author_GND | (DE-588)103337075 |
| author_facet | Vainikko, Gennadi 1938- |
| author_role | aut |
| author_sort | Vainikko, Gennadi 1938- |
| author_variant | g v gv |
| building | Verbundindex |
| bvnumber | BV007745899 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)246274274 (DE-599)BVBBV007745899 |
| dewey-full | 510 515/.45 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510 515/.45 |
| dewey-search | 510 515/.45 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV007745899 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:37:41Z |
| institution | BVB |
| isbn | 3540568786 0387568786 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005093366 |
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| owner | DE-384 DE-20 DE-12 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-824 DE-706 DE-634 DE-83 DE-188 DE-11 |
| owner_facet | DE-384 DE-20 DE-12 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-824 DE-706 DE-634 DE-83 DE-188 DE-11 |
| physical | XI, 158 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Vainikko, Gennadi 1938- Verfasser (DE-588)103337075 aut Multidimensional weakly singular integral equations Gennadi Vainikko Berlin u.a. Springer 1993 XI, 158 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1549 Algorithmee cubature Jussieu Analyse numérique Jussieu Approximation solution Jussieu Collocation Jussieu Convergence discrète Jussieu Equation intégrale Peierls Jussieu Equation intégrale faiblement singulière Jussieu Equation intégrale non linéaire Jussieu Integraalvergelijkingen gtt Interpolation Jussieu Transfert radiatif Jussieu Équations intégrales - Théorie asymptotique Équations intégrales - Théorie asymptotique ram Integral equations Asymptotic theory Schwache Singularität (DE-588)4180293-7 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Diskretisierung (DE-588)4012469-1 gnd rswk-swf Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Integralgleichung (DE-588)4027229-1 s Schwache Singularität (DE-588)4180293-7 s Diskretisierung (DE-588)4012469-1 s DE-604 Asymptotische Methode (DE-588)4287476-2 s Lecture notes in mathematics 1549 (DE-604)BV000676446 1549 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005093366&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vainikko, Gennadi 1938- Multidimensional weakly singular integral equations Lecture notes in mathematics Algorithmee cubature Jussieu Analyse numérique Jussieu Approximation solution Jussieu Collocation Jussieu Convergence discrète Jussieu Equation intégrale Peierls Jussieu Equation intégrale faiblement singulière Jussieu Equation intégrale non linéaire Jussieu Integraalvergelijkingen gtt Interpolation Jussieu Transfert radiatif Jussieu Équations intégrales - Théorie asymptotique Équations intégrales - Théorie asymptotique ram Integral equations Asymptotic theory Schwache Singularität (DE-588)4180293-7 gnd Integralgleichung (DE-588)4027229-1 gnd Diskretisierung (DE-588)4012469-1 gnd Asymptotische Methode (DE-588)4287476-2 gnd |
| subject_GND | (DE-588)4180293-7 (DE-588)4027229-1 (DE-588)4012469-1 (DE-588)4287476-2 |
| title | Multidimensional weakly singular integral equations |
| title_auth | Multidimensional weakly singular integral equations |
| title_exact_search | Multidimensional weakly singular integral equations |
| title_full | Multidimensional weakly singular integral equations Gennadi Vainikko |
| title_fullStr | Multidimensional weakly singular integral equations Gennadi Vainikko |
| title_full_unstemmed | Multidimensional weakly singular integral equations Gennadi Vainikko |
| title_short | Multidimensional weakly singular integral equations |
| title_sort | multidimensional weakly singular integral equations |
| topic | Algorithmee cubature Jussieu Analyse numérique Jussieu Approximation solution Jussieu Collocation Jussieu Convergence discrète Jussieu Equation intégrale Peierls Jussieu Equation intégrale faiblement singulière Jussieu Equation intégrale non linéaire Jussieu Integraalvergelijkingen gtt Interpolation Jussieu Transfert radiatif Jussieu Équations intégrales - Théorie asymptotique Équations intégrales - Théorie asymptotique ram Integral equations Asymptotic theory Schwache Singularität (DE-588)4180293-7 gnd Integralgleichung (DE-588)4027229-1 gnd Diskretisierung (DE-588)4012469-1 gnd Asymptotische Methode (DE-588)4287476-2 gnd |
| topic_facet | Algorithmee cubature Analyse numérique Approximation solution Collocation Convergence discrète Equation intégrale Peierls Equation intégrale faiblement singulière Equation intégrale non linéaire Integraalvergelijkingen Interpolation Transfert radiatif Équations intégrales - Théorie asymptotique Integral equations Asymptotic theory Schwache Singularität Integralgleichung Diskretisierung Asymptotische Methode |
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