A numerical method for solving a complete hypersingular integral equation of the second kind and its justification
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 tha...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2023-10-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://jau.vgtu.lt/index.php/MMA/article/view/14761 |
| Summary: | 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.
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| ISSN: | 1392-6292 1648-3510 |