Discrete Model Solving Time-Dependent Matrix Eigen Problem with ZeaD (Zhang et al Discretization) Formula Using 7 Points

In this paper, the problem of computing time-dependent eigenvalues and eigenvectors is investigated using ZD (Zhang dynamics) method. A new 7-point ZeaD (Zhang et al discretization) formula is then proposed. The ZeaD formula is used to derive a discrete ZD model for computing the time-dependent eigenvalues and eigenvectors, which is termed as discrete ZD solution model (DZDSM). DZDSM parameters are optimized, and the model has a good performance in double precision arithmetic. Numerical experiments are also conducted. As learned from numerical results, the truncation error of the DZDSM almost reaches the boundary of double precision with a small enough sampling gap. Besides, numerical results also verify the theory of truncation error and optimized parameters.