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

Abstract

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.

Keywords

• complete hypersingular integral equation
• singular integral
• integral with the logarithmic kernel
• numerical method
• Nyström-type
• existence