摘要
本文通过对四次Lagrange插值多项式求二次导数推导出二阶导数的五点数值微分公式,中心点处截断误差为O(h4),其他点处为O(h3).利用Richardson外推原理得到该公式各个点的外推算法,K次外推后,中间节点的数值精度提高到O(h2(k+2)),其他节点的精度提高到O(hk+3).
The five-point formulas for two-order derivative are obtained by the interpolation polynomial. The extrapolation methods of formulas are obtained by Richardson extrapolation method. After k times extrapolation, the truncation error of the middle point is improved from O（ h^4 ） to O（h^2（k＋2 ） , the truncation error of the others arc improved from O（ h^3 ） to O（ h^k ＋3 ）.
出处
《天津理工大学学报》
2009年第4期37-39,共3页
Journal of Tianjin University of Technology
