中文摘要：

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．

英文摘要：

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.