Work

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

Year: 2024

Type: article

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.

Source: Mathematics

DOI: 10.3390/math12182920

Authors: Muhammad Zakria Javed, Muhammad Uzair Awan, Bandar Bin-Mohsin, Savin Treanţă

Institutions: Government College University, Faisalabad, King Saud University, Academia Oamenilor de Știință din România, Universitatea Națională de Știință și Tehnologie Politehnica București

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funder: King Saud University