Algorithm for construction of quadrature formulas with exponential convergence for linear operators acting on periodic functions

The algorithm of the derivation of quadrature formulas for the calculation of linear operators acting on periodic functions is presented. For analytic functions, the order of accuracy of quadrature formulas increases indefinitely with the number of grid nodal points increasing. With sufficiently general restrictions on the kernels of linear operators, an exponential valuation of the quadrature formula has been proved. As examples, the quadrature formulas for the calculation of integral operators with logarithmic singularities used in the boundary element method to derive superconvergent numerical schemes for solving boundary value problems of harmonic and biharmonic equations on the plane, have been obtained.