On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

Anton V. Voytishek, Nikolay M. Shipilov

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationProceedings of the 8th International Conference on Mathematical Modeling, ICMM 2017
EditorsIE Egorov, SV Popov, PN Vabishchevich, MY Antonov, NP Lazarev, MS Troeva, MS Troeva, AO Ivanova, YM Grigorev
PublisherAmerican Institute of Physics Inc.
Number of pages15
Volume1907
ISBN (Electronic)9780735415997
DOIs
Publication statusPublished - 14 Nov 2017
Event8th International Conference on Mathematical Modeling, ICMM 2017 - Yakutsk, Russian Federation
Duration: 4 Jul 20178 Jul 2017

Publication series

NameAIP Conference Proceedings
PublisherAMER INST PHYSICS
Volume1907
ISSN (Print)0094-243X

Conference

Conference8th International Conference on Mathematical Modeling, ICMM 2017
CountryRussian Federation
CityYakutsk
Period04.07.201708.07.2017

Keywords

  • Fredholm integral equation of the second kind
  • numerical solution
  • randomized algorithms
  • projection
  • mesh
  • projection-mesh algorithms
  • important (actual) applied problems: computability of kernel and free term of an equation

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