We consider an initial boundary value problem for parabolic equation in the planar double-connected domain with the Dirichlet and the Neumann boundary value conditions. This mixed problem is reduced by Rothe"s method to the sequence of elliptic boundaryvalue problems with first and second orders of the time approximation. Then the indirect boundary integral equation method is used. The boundary layer potentials are constructed using the fundamental solutions of the sequence of the elliptic equations. The obtained integral equations of the first kind contain the logarithmic and hypersingular kernels. They are solved by a discrete collocation method based on trigonometrical quadratures. The presented numerical experiments confirm a posterior error estimates and show the feasibility of the proposed method.
