Presentation, Derivation and Numerical Experiments of a Group of Extrapolation Formulas
Yunong Zhang, Zhicheng Yang, Jianrong Chen, Zhiyuan Qi, Guanqun Yang · 2019
In this paper, Taylor expansion and Vandermonde determinant are used to derive the coefficients of the group of extrapolation formulas. In the derivation of the coefficients, we first use Taylor expansion to expand the formulas, then the expansion is transformed into Vandermonde matrix. The general formula of coefficients is obtained by using the characteristics of Vandermonde determinant and Cramer's rule. After careful observation, we find that the rule of the coefficients is similar to that of Pascal's triangle. Three functions are used in numerical experiments. We first evaluate the effect of different step size values on error using order-3 formula, and then we evaluate the effect of different order formulas on error with some fixed step size value.