A new diffusion-transport hybrid nodal method in R-Z is presented that can effectively treat non-multiplying zones in pebble bed reactors. The new method seamlessly combines the analytic coarse mesh finite difference (CMFD) diffusion formulation and a transport theory based response matrix formulation while retaining the properties and structure of the CMFD diffusion solver. The resulting combined formulation is utilized in selected non-multiplying nodes to capture angular effects on the flux. Test results indicate that the method has been implemented correctly into the CYNOD reactor kinetics code. This document also presents a status report on the development of a better source approximation for the Green’s function nodal solution in the radial direction of cylindrical geometry. The basic theory has been developed, including obtaining polynomials that are orthonormal over the domain of integration and the derivation of approximately half of the required matrix elements (single and double integrals in the source expansions).