Classification and Applications of Randomized Functional Numerical Algorithms for the Solution of Second-Kind Fredholm Integral Equations

Research output: Contribution to journalArticlepeer-review

Abstract

Systematization of numerical randomized functional algorithms for approximation of solutions to second-kind Fredholm integral equation is performed in this paper. Three types of algorithms are emphasized: projection algorithms, grid algorithms, and projection-grid algorithms. Disadvantages of grid algorithms that require calculation of values of the kernel of integral equations at fixed points are revealed (practically, the kernels of equation have integrable singularities and this calculation is impossible). Thus, for applied problems related to the solution of second-kind Fredholm integral equations, projection or projection-grid randomized algorithms are more convenient.

Original languageEnglish
Pages (from-to)589-605
Number of pages17
JournalJournal of Mathematical Sciences (United States)
Volume254
Issue number5
DOIs
Publication statusPublished - May 2021

Keywords

  • 45B05
  • 65C05
  • 65C40
  • computational kernel
  • grid algorithm
  • numerical solution
  • projection algorithm
  • randomized algorithm
  • second-kind Fredholm integral equation

OECD FOS+WOS

  • 1.01 MATHEMATICS
  • 1.01.XY STATISTICS & PROBABILITY
  • 1.01.PN MATHEMATICS, APPLIED

Fingerprint

Dive into the research topics of 'Classification and Applications of Randomized Functional Numerical Algorithms for the Solution of Second-Kind Fredholm Integral Equations'. Together they form a unique fingerprint.

Cite this