Mixed Boundary Value Problems occur, in a natural way, in varieties of
branches of physics and engineering and several mathematical methods
have been developed to solve this class of problems of applied
mathematics. While understanding applications of such boundary value
problems are of immense value to physicists and engineers, analyzing
these problems mathematically and determining their solutions by
utilizing the most appropriate analytical or numerical methods are the
concerns of applied mathematicians. Of the various analytical methods,
which are useful to solve certain mixed boundary value problems arising
in the theory of scattering of surface water waves, the methods
involving complex function theory and singular integral equations will
be examined in detail along with some recent developments of such
methods.
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