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A hypersingular integral equation in two disjoint intervals is solved by using the solution of Cauchy type singular integral equation in disjoint intervals. Also a direct function theoretic method is used to determine the solution of the same hypersingular integral equation in two disjoint intervals. Solutions by both the methods are in good agreement with… (More)
A direct function theoretic method is applied to solve a weakly singular integral equation whose kernel involves logarithmic singularity. This method avoids the occurrence of strong singularity. The solution of this integral equation is then applied to re-investigate the well known problem of water wave scattering by a partially immersed vertical barrier.
In the present paper, the solution of a singular integral equation with logarithmic kernel in two disjoint intervals (0, a)4(b, ∞), (a, b are finite) is obtained by using function theoretic method. The two cases are considered when the unknown function satisfying the integral equation is unbounded or bounded at both nonzero finite end points of the… (More)
We used function theoretic method to solve a singular integral equation with logarithmic kernel in two disjoint finite intervals where the unknown function satisfying the integral equation may be bounded or unbounded at the nonzero finite endpoints of the interval concerned. An appropriate solution of this integral equation is then applied to solve the… (More)
Water wave scattering by an uneven dock is investigated here. Using a simplified perturbation analysis, the first order correction to the reflection coefficient is obtained in terms of an integral involving the shape function describing the dock topography. The first order reflection coefficient is depicted graphically for two shape functions of the dock… (More)