A Numerical Method for Solving a Complete Hypersingular Integral Equation of the Second Kind and Its Justification

被引：1

作者：

V. Kostenko, Oleksii ^{[1
]}

机构：

[1] Natl Acad Sci Ukraine, B Verkin Inst Low Temp Phys & Engn, 47 Nauky Ave, UA-61103 Kharkiv, Ukraine

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2023年 / 28卷 / 04期

关键词：

logarithmic kernel; numerical method; Nystro center dot m-type; existence; uniqueness; convergence; rate; model problem; RESONANCES; STRIPS;

D O I：

10.3846/mma.2023.14761

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Nystrom. 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.

引用

页码：689 / 714

页数：26

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