Theoretical Analyses and Results of Taylor-Zhang Discretization Formula and ZeaD4Ig2_Y Formula Generating Discrete-Time Solutions of ODE Dynamic Systems

In this paper, a Zhang et al discretization (ZeaD) formula termed ZeaD with 4 instants, g square and Y subtype (ZeaD4Ig2\_Y), where g denotes the sampling gap, which can effectively approximate the 1st-order time derivative with square truncation error pattern, is presented and investigated. By adopting the ZeaD4Ig2\_Y formula, a new method for generating discrete-time solutions of ordinary differential equation (ODE, more rigorously, ordinary derivative equation, or ordinary differential-quotient equation) is proposed and analyzed. For purpose of comparison, the conventional Euler method and Taylor-Zhang method for solving ODE are also presented in this paper. In addition, theoretical analyses and results show that the final global error (FGE) of the ZeaD4Ig2\_Y method has a square pattern, whereas the FGE of the Euler method has a linear pattern.