An approximate solution of one class of singular integro-differential equations

The problem of definition of mechanical field in a homogeneous plate supported by finite inhomogeneous inclusion is considered. The contact between the plate and inclusion is realized by a thin glue layer. The problem is reduced to the boundary value problem for singular integro-differential equations. Asymptotic analysis is carried out. Using the method of orthogonal polynomials, the problem is reduced to the solution of an infinite system of linear algebraic equations. The obtained system is investigated for regularity.