中山大学学报（自然科学版）2012，Vol.51Issue(2)：1-5,5.
一点超前数值差分公式的提出、研究与实践
Proposing, Investigation and Practice on One-Node-Ahead Numerical Differentiation Formulas
摘要
Abstract
Based on the numerical differential theory, it is available to calculate the approximate first derivative of the target-node by using numerical differentiation formulas when the discrete sampling points of the unknown target function on specified interval are given. But for the target-nodes close to the boundary , it may be unable to use the center differentiation formulas involving multiple nodes because of the lack of sampling points on one side of the target-node. Besides, an accelerating change of the first derivative of the target-node may occur in some target functions. However, the use of forward/backward differentiation formulas simply takes the nodes on one side of the target-node into consideration, which probably makes the formulas difficult to adapt to such a change, and thus leads to less accuracy in estimating the first derivative of the target-node. Actually, for the target-nodes close to the right boundary, it is available to move the backward differentiation formulas one node ahead to calculate the first derivatives. Therefore, one-node-ahead numerical differentiation formulas are proposed and investigated. Experimental results verify and show that the first derivatives of the target-nodes with high computational precision can be obtained by using the one-node-ahead numerical differentiation formulas.关键词
未知目标函数/一阶导数/一点超前/数值差分公式/计算精度Key words
unknown target function/ first derivatives/ one node ahead/ numerical differentiation formulas/ computational precision分类
数学引用本文复制引用
张雨浓,陈宇曦,陈锦浩,殷勇华..一点超前数值差分公式的提出、研究与实践[J].中山大学学报（自然科学版）,2012,51(2):1-5,5.基金项目
国家自然科学基金资助项目(61075121) （61075121）
教育部高等学校博士学科点专项科研基金博导类资助项目(20100171110045) （20100171110045）
