Upper Bounds for the Remainder Term in Boole’s Quadrature Rule and Applications to Numerical Analysis

Muhammad Zakria Javed, Muhammad Uzair Awan (), Bandar Bin-Mohsin () and Savin Treanţă
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Muhammad Zakria Javed: Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
Muhammad Uzair Awan: Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
Bandar Bin-Mohsin: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Savin Treanţă: Faculty of Applied Sciences, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania

Mathematics, 2024, vol. 12, issue 18, 1-20

Abstract: In the current study, we compute some upper bounds for the remainder term of Boole’s quadrature rule involving convex mappings. First, we build a new identity for first-order differentiable mapping, an auxiliary result to establish our required estimates. We provide several upper bounds by utilizing the identity, convexity property, and bounded property of mappings and some well-known inequalities. Moreover, based on our primary findings, we deliver applications to the means, quadrature rule, special mappings, and non-linear analysis by developing a novel iterative scheme with cubic order of convergence. To the best of our knowledge, the current study is the first attempt to derive upper bounds for Boole’s scheme involving convex mappings.

Keywords: Boole’s rule; convex mapping; iterative methods; inequality; quadrature rule; basins of attraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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