The problem of numerical realization of integral operators of axisymmetric boundary value problems (algorithms without saturation)

In the paper a fundamentally new, unsaturated, method of numerical implementation integral operators of $C^\infty$-smooth axisymmetric boundary value problems is described. The method allows one to take into account the specifics of the axisymmetric problems automatically. This specifics is an obstacle to any numerical methods with the principal term of error.
The method was extensively tested on the problem of precise evaluation of the Gauss integral of the theory of harmonic potential in high aspect ratio ellipsoids.