A new DTZD algorithm with geometric representation and numerical verification for solving time-varying nonlinear equations

Recently, a new class of neural dynamics, which is called Zhang dynamics (ZD), has been studied for online solution to time-varying nonlinear equations. By following the previous research, this study proposes a new discrete-time ZD (DTZD) algorithm for solving time-varying nonlinear equations. Such a DTZD algorithm is the discretization of the previous continuous-time ZD (CTZD) model via the Taylor-type difference rule. Then, the computational performance of the proposed algorithm is theoretically analyzed. This DTZD algorithm is also represented in a geometric way. Numerical results further demonstrate the effectiveness of the proposed DTZD algorithm in finding the roots of time-varying nonlinear equations.