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 -