The work contains the approximation of the third boundary value problem of schemes of high order. The approximation of the operator of the convective and diffusive transport difference schem were obtained, which has the fourth-order approximation error. The discrete operator diffusive transport in the absence of the influence of the boundary was considered.The construction of schemes of higher order accuracy approximates the operator diffusive transport in the border nodes in the case of boundary conditions of the third kind with the second order of accuracy was found.

Keywords: Schemes of high order, diffusion, diffusion transfer, discrete operator, approximation, boundary conditions, boundary value problem, finite-difference scheme