论文标题
有限差异和数值差异：递延校正的一般公式
Finite difference and numerical differentiation: General formulae from deferred corrections
论文作者
论文摘要
本文提供了一种新的方法，用于得出各种任意高阶有限差差公式，以换取分析函数的数值差异。在这种方法中，用于分析函数的数值近似的各种一阶和二阶公式，以明确扩展为泰勒分析函数的泰勒级数的误差项给出。这些较低的近似值将一两个或两个（中心公式的两个顺序改进）依次改善，以提供任意高阶的有限差差公式。新方法允许以正式的有限差分运算符的形式功率系列来恢复标准的后退，向前和中心有限差异公式。给出了适合递延校正方法的新公式的示例。
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical approximation of analytic functions are given with error terms explicitly expanded as Taylor series of the analytic function. These lower order approximations are successively improved by one or two (two order improvement for centered formulae) to give finite difference formulae of arbitrary high order. The new approach allows to recover the standard backward, forward, and centered finite difference formulae which are given in terms of formal power series of finite difference operators. Examples of new formulae suited for deferred correction methods are given.
