Development of a computational technique for the analysis of quasi-normal modes in hybrid-plasmonic resonators is the main goal of this research. Because of the significant computational costs of this analysis, one has to take various symmetries of these resonators into account. In this research, we consider cylindrical symmetry of hybrid-plasmonic ring resonators and implement a body-of-revolution finite-difference time-domain (BOR-FDTD) technique to analyze these resonators. We extend the BOR-FDTD method by proposing two different sets of auxiliary fields to implement multi-term Drude-Lorentz and multi-term Lorentz models in BOR-FDTD. Moreover, we utilize the filter-diagonalization method to accurately compute the complex resonant frequencies of the resonators. This approach improves numerical accuracy and computational time compared to the Fourier transform method used in previous BOR-FDTD methods. Our numerical analysis is verified by a 2D axisymmetric solver in COMSOL Multiphysics.