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(tau(2)) error pattern, where tau denotes the sampling gap. In this paper, by exploiting the Taylor-type difference rule, a new three-step DTZD algorithm with O(tau(3)) 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. (C) 2016 Elsevier B.V. All rights reserved.