摘要
传统的数值微分公式有前向差分、后向差分和中心差分公式.所谓一点超前差分公式,就是后向差分公式在形式上"前移"一点来计算一阶导数的公式.该公式有效地弥补了传统差分公式的不足之处.不同于以前研究中使用拉格朗日公式来推导一点超前公式的做法,给出了基于泰勒级数展开的对该组公式及其截断误差的推导,从另一个角度验证了一点超前公式,使其更为完善.
Traditional numerical differentiation formulas include forward, backward and central difference formulas. One-node-ahead difference formulas are formed by moving the backward difference formulas one node ahead to calculate the first derivatives. One-node-ahead formulas can effectively remedy the deficiency of traditional formulas. Different from previous work which derives one-node-ahead formulas based on Lagrange polynomial,we propose an alternative derivation of the formulas and truncation error based on Taylor series expansion. We prove the one-node-ahead formulas from another perspective,which makes them more complete.
出处
《大学数学》
2014年第1期12-16,共5页
College Mathematics
基金
国家自然科学基金(61075121)
教育部高等学校博士学科点专项科研基金博导类课(2010017111045)
国家大学生创新训练项目(201210558042)
关键词
数值差分公式
泰勒级数
一阶导数
一点超前
截断误差
numerical difference {ormulas
Taylor series
first derivative
one node ahead
truncation error
