Geodesic
Development and optimization of randomized functional numerical methods for solving the practically significant Fredholm integral equations of the second kind
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 2, pp. 32-45

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Under study are the randomized algorithms for numerical solution of the Fredholm integral equations of the second kind (from the viewpoint of their application for the practically important problems of mathematical physics) are studied. The projection, grid and projection-grid methods are distinguished. Certain advantages of the projection and projection-grid methods are demonstrated (allowing using them for numerical solution of the equations with the integrable singularities in kernels and free terms).
Keywords: applied Fredholm integral equations of the second kind, integrable singularity, numerical randomized functional method, projection, grid, projection-grid functional algorithm. 
@article{SJIM_2018_21_2_a2,
     author = {A. V. Voytishek},
     title = {Development and optimization of randomized functional numerical methods for solving the practically significant {Fredholm} integral equations of the second kind},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {32--45},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_2_a2/}
}
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A. V. Voytishek. Development and optimization of randomized functional numerical methods for solving the practically significant Fredholm integral equations of the second kind. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 2, pp. 32-45. http://geodesic.mathdoc.fr/item/SJIM_2018_21_2_a2/