In this paper, we give some refinements of Simpson’s rule in cases when it is not applicable in its classical form i.e., when the target function is not four times differentiable on a given interval. Some sharp two-sided inequalities for an extended form of Simpson’s rule are also proven.

中文翻译：

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辛普森法则重新审视

在本文中，我们对辛普森规则进行了一些改进，以防它不适用于其经典形式，即目标函数在给定区间上不是四次可微的。辛普森规则的扩展形式的一些尖锐的双边不等式也被证明。