TL;DR
This paper presents refined versions of Simpson's Rule for functions lacking fourfold differentiability and establishes sharp inequalities for its extended form.
Contribution
It introduces refinements of Simpson's Rule applicable to less smooth functions and proves sharp inequalities for its extended version.
Findings
Refined Simpson's Rule for non-four-times differentiable functions
Sharp two-sided inequalities for extended Simpson's Rule
Broader applicability of Simpson's Rule in numerical integration
Abstract
In this article we give some refinements of Simpson's Rule in cases when it is not applicable in it's 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.
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