Taylor-Zhang Discretization Formula Extended to Time-Varying Four Fundamental Operations with Numerical Experiments

摘要

Discrete time-varying problems are frequently encountered in mathematics and engineering fields, such as numerical analysis, signal processing and computer computing. However, conventional algorithms mainly solve time-invariant problems. Employed for discrete time-varying problems solving, conventional algorithms may generate quite large and unacceptable lagging errors. In this paper, discrete time-varying four fundamental operations (DTVFFOs) are studied. In order to eliminate the lagging errors, based on the zeroing dynamics (ZD) and Taylor-Zhang discretization formula, discrete computing models, which are termed T-Z-K and T-Z-U models, are proposed and investigated. Note that the aforementioned models have an error pattern of O(g~3), where g denotes the sampling gap. For comparison, Euler-type discrete models and Newton iteration (NI) models are also presented. Eventually, illustrative numerical experiments are displayed to testify the great performances of the proposed Taylor-Zhang discrete ZD models.