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

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 a...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 254; no. 5; pp. 589 - 605
Main Author Voytishek, A. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2021
Springer
Springer Nature B.V
Subjects
Algorithms
Fredholm equations
Integral equations
Kernels
Mathematics
Mathematics and Statistics
Projection
numerical solution
65C40
grid algorithm
computational kernel
45B05
randomized algorithm
65C05
projection algorithm
second-kind Fredholm integral equation
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05328-z