Discrete-Time ODE Solutions Generated by TZD and ZeaD4Ig2_Y Formulas: Numerical Results

ZeaD4Ig2_Y formula, a recently new Zhang et al discretization (ZeaD) formula termed with 4-instant, g-square truncation error and Y-subtype, can effectively approximate the first-order derivative. In this paper, aiming at generating the discrete-time ordinary differential equation (ODE) solutions, the ZeaD4Ig2_Y method is presented and investigated through applying the ZeaD4Ig2_Y formula. Meanwhile, the Euler method and the Taylor-Zhang discretization (TZD) method are also presented for comparison and evaluation. More specifically, detailed discretization experiments are conducted and discussed to substantiate the efficacy and accuracy of the ZeaD4Ig2_Y method for solving ODE in discrete time; i.e., the discrete-time ODE solutions can converge to the theoretical solutions effectively.