A high order transport approximation, the SK[subscript]N approximation, a mnemonic for "synthetic kernel", is suggested for solving the integral transport equation. The method relies on approximating the integral transport kernels by a sum of diffusion-like kernels. The integral equation is then reducible to a set of coupled differential equations, and the boundary conditions (black body and reflecting boundary conditions) are established. These equations, the SK[subscript]N equations, are solved for benchmark problems. The benchmark problems include one- and two-dimensional homogeneous and heterogeneous cell configurations found in nuclear reactor applications. The solutions of the benchmark problems are compared against integral equation, S[subscript]N, nodal P[subscript]N and Monte-Carlo solutions.