On a weakly singular integral equation and its application

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.

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[2]  F. Ursell,et al.  Multipole expansions in the theory of surface waves , 1953, Mathematical Proceedings of the Cambridge Philosophical Society.