Abstract
An interesting identity for 3-point Gauss-Legendre quadrature rule using functions that are n-times differentiable. By applying the established identity, a sharp inequality which gives an error bound for 3-point Gauss-Legendre quadrature rule and some generalizations are derived. At the end, an application in numerical integration is given.
Highlights
Inequalities play a main role in error estimations
The same practice when the formulas are combined to form the composite rules, but this restriction can significantly decrease the accuracy of the approximation
In order to investigate 2—point Gauss—Legendre quadrature rule, Ujevic in [8], obtained bounds for absolutely continuous functions with derivatives which belong to L2(a, b), as follows: Theorem 1.1
Summary
Inequalities play a main role in error estimations. A few years ago, by using modern theory of inequalities and Peano kernel approach a number of authors in [2, 3, 4, 6, 7] have considered an error analysis of some quadrature rules of Newton—Cotes type. In order to investigate 2—point Gauss—Legendre quadrature rule, Ujevic in [8], obtained bounds for absolutely continuous functions with derivatives which belong to L2(a, b), as follows: Theorem 1.1. To support our results and to mention which of them is better from the point of view of the best estimator and to mention that for certain types of functions they may not be applicable an application in numerical integration is given. These results may motivate further research in different areas of pure and applied sciences
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