Geodesic
Approximate solution of the smooth transition equation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1849-1862

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The problems of stability and the approximate solution of the integral smooth transition equation first introduced and studied by Yu.I. Chersky are considered. Using the solution of the smooth transition equation under classical assumptions, it is possible to construct the solution of the equation under weaker constraints on the kernels. For the approximate solution, an error estimation and a theorem on the uniqueness and sustainability are provided.
Keywords: smooth transition integral equation, approximate solution, iterative algorithms, stability. 
@article{SEMR_2020_17_a104,
     author = {V. A. Lukianenko},
     title = {Approximate solution of the smooth transition equation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1849--1862},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a104/}
}
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V. A. Lukianenko. Approximate solution of the smooth transition equation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1849-1862. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a104/