Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind. / Voytishek, Anton V.; Shipilov, Nikolay M.
Proceedings of the 8th International Conference on Mathematical Modeling, ICMM 2017. ред. / IE Egorov; SV Popov; PN Vabishchevich; MY Antonov; NP Lazarev; MS Troeva; MS Troeva; AO Ivanova; YM Grigorev. Том 1907 American Institute of Physics Inc., 2017. 030015 (AIP Conference Proceedings; Том 1907).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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TY - GEN
T1 - On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind
AU - Voytishek, Anton V.
AU - Shipilov, Nikolay M.
PY - 2017/11/14
Y1 - 2017/11/14
N2 - In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.
AB - In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.
KW - Fredholm integral equation of the second kind
KW - numerical solution
KW - randomized algorithms
KW - projection
KW - mesh
KW - projection-mesh algorithms
KW - important (actual) applied problems: computability of kernel and free term of an equation
UR - http://www.scopus.com/inward/record.url?scp=85036555981&partnerID=8YFLogxK
U2 - 10.1063/1.5012637
DO - 10.1063/1.5012637
M3 - Conference contribution
AN - SCOPUS:85036555981
VL - 1907
T3 - AIP Conference Proceedings
BT - Proceedings of the 8th International Conference on Mathematical Modeling, ICMM 2017
A2 - Egorov, IE
A2 - Popov, SV
A2 - Vabishchevich, PN
A2 - Antonov, MY
A2 - Lazarev, NP
A2 - Troeva, MS
A2 - Troeva, MS
A2 - Ivanova, AO
A2 - Grigorev, YM
PB - American Institute of Physics Inc.
T2 - 8th International Conference on Mathematical Modeling, ICMM 2017
Y2 - 4 July 2017 through 8 July 2017
ER -
ID: 9648148