An effective method of solving of singular integral equations in mechanical problems with mixed boundary conditions

A two-dimensional singular integral equation in a rather arbitrary symmetrical area is considered, to which some problems of mechanics with mixed boundary conditions are reduced. Particularly, these include, the problem of the plate's plane struck on the flat surface of an incompressible fluid, as well as the problem of a plane crack of normal rupture in an unbounded elastic medium. Special presentation of the kernel of integral equation is able to significantly weaken its singularity, which in turn helped to realize a sustainable computing process by collocation method.