Theoretical analysis, numerical verification and geometrical representation of new three-step DTZD algorithm for time-varying nonlinear equations solving

To solve time-varying nonlinear equations, Zhang et al. have developed a one-step discrete-time Zhang dynamics (DTZD) algorithm with O(τ2) error pattern, where τ denotes the sampling gap. In this paper, by exploiting the Taylor-type difference rule, a new three-step DTZD algorithm with O(τ3) error pattern is proposed and investigated for time-varying nonlinear equations solving. Note that such an algorithm can achieve better computational performance than the one-step DTZD algorithm. As for the proposed three-step DTZD algorithm, theoretical results are given to show its excellent computational property. Comparative numerical results further substantiate the efficacy and superiority of the proposed three-step DTZD algorithm for solving time-varying nonlinear equations, as compared with the one-step DTZD algorithm. Besides, the geometric representation of the proposed three-step DTZD algorithm is provided for time-varying nonlinear equations solving.