A numerical method for solving a complete hypersingular integral equation of the second kind and its justification

Autor:	Oleksii V. Kostenko
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	complete hypersingular integral equation singular integral integral with the logarithmic kernel numerical method Nyström-type existence Mathematics QA1-939
Zdroj:	Mathematical Modelling and Analysis, Vol 28, Iss 4 (2023)
Druh dokumentu:	article
ISSN:	1392-6292 1648-3510
DOI:	10.3846/mma.2023.14761
Popis:	A complete hypersingular integral equation of the second kind was obtained as a boundary integral equation for the diffraction and scattering problem of electromagnetic waves in space separated by the periodically placed non-perfectly conducting strips. The equation includes a singular integral that distinguishes it from the studied second-kind hypersingular equation. Our motivation is the need to have a numerical method for the equation, its applicability borders, and guaranteed convergence. The numerical method has the type of Nyström. The justification of the method envelops a proof of the theorem of existence and uniqueness of the solution and an estimate of the convergence rate of sequence of the approximate solutions to an exact solution.
Databáze:	Directory of Open Access Journals
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