Abstract: The BN stable method is a new type of time integration method for solving dynamic problems, which can be used to accurately and efficiently solve complex nonlinear vibration problems. Since its proposal in 2021, this type of solution methods has received attention from academic communities. This article discusses the design idea, solution schemes and parameter optimization principle of the BN-stable method. Using higher-order nonlinear single-degree-of-freedom system and rigid satellite as examples, the BN-stable method is compared with the classical Generalized-α method and the ρ_∞-Bathe method, and comparison results show that the BN-stable method has considerable advantages both in accuracy and stability. Further, this work can provide innovative materials for the course of vibration mechanics, in order to cultivate students' innovative ability and analytical ability for nonlinear vibration problems.