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This paper proposes a method for the stability analysis of dynamic neural networks. The stability analysis of dynamic neural networks is a challenging task due to internal feedback connections. In this research work, we propose an algorithm based on the Reduction of Dissipativity Domain (RODD) algorithm. The RODD algorithm is a numerical technique for the detection of the stability of nonlinear dynamic systems. The method works by using an approximation of the reachable set. This paper proposes linear and quadratic approximations of reachable sets. RODD-LB uses a linear approximation, RODD-EB uses a quadratic approximation, and the RODD-Hybrid algorithm uses a combination of the linear and quadratic approximations. The accuracy and convergence of these algorithms were derived through numerical dynamic systems.