一阶导数的五点数值微分公式及外推算法  

The Extrapolation Method of Five-Point Numerical Formulas for One-Order Derivative

作　　者：王燕[1] 

机构地区：[1]宁夏大学数学计算机学院,宁夏银川750021

出　　处：《数学的实践与认识》2011年第6期163-167,共5页Mathematics in Practice and Theory

基　　金：宁夏大学自然科学基金(NDZR10-36)

摘　　要：通过对四次Lagrange插值多项式求导推导出一阶导数的五点数值微分公式,其截断误差为O(h^4).利用Richardson外推原理得到该公式的外推算法,K次外推后,中间节点的数值精度提高到O(h^(2(k+2))),其它节点的精度提高到O(h^(k+4)).Abstract： The five-point formulas for one-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（h4） to O（h2（k＋2））, the truncation error of the others are improved from O（h4） to O（hk＋4））.

关 键 词：插值多项式 Richardson外推算法 五点数值微分公式 

分 类 号：O172.1[理学—数学]