hypersingular integral equations; boundary perturbation method; expansion-collocation method; Chebyshev polynomials; Gegenbauer polynomials; water waves
The problem of a solving a class of hypersingular integral equations over the boundary of a nonplanar disc is considered. The solution is obtained by an expansion in basis functions that are orthogonal over the unit disc. A Fourier series in the azimuthal angle, with the Fourier coefficients expanded in terms of Gegenbauer polynomials is employed. These integral equations appear in the study of the interaction of water waves with submerged thin plates.