[en] This paper presents a unified formulation of the Nodal Expansion Method (NEM) and Nodal Green's Function Method (NGFM) in Cartesian geometry although there is a significant difference between them. Both methods employ the same inner iterative scheme namely Row-Column iteration strategy to solve the interface current equation. It's generally believed that the NEM is somewhat faster than the NGFM. However, calculations of IAEA3D benchmark problem carried out by newly implemented NGFM and NEM show that not only the accuracy but also the performance of the NGFM are better than that of the NEM in Cartesian geometry. Both the NGFM and NEM are extended to solve neutron diffusion equation in cylindrical geometry. Since the traditional transverse integration fails to produce a 1-D transverse integrated equation in Θ-direction, a simple approach is introduced to obtain this equation in Θ-direction. The 1-D transverse integrated equations in r-direction are solved by the NEM using the special polynomials and by the NGFM using Green's function based on modified Bessel function respectively. The same iterative scheme employed for Cartesian geometry can be readily applied to the cylindrical geometry case. The Cylindrical Nodal Expansion Method (CNEM) and the Cylindrical Nodal Green's Function Method (CNGFM) codes are developed and applied to Dodd's r-z benchmark problem. The results show that both the CNEM and CNGFM are capable of very high performance and accuracy in cylindrical geometry. Meanwhile this paper demonstrates that nodal methods have prominent advantages over traditional finite difference method in both Cartesian geometry and cylindrical geometry. (authors)