Error Bounds of Boole's Formula for Twice Differentiable Convex Functions with Numerical Analysis

Wali Haider; Hüseyin Budak; Asia Shehzadi; Muhammad Toseef

doi:10.14244/lajm.v5i1.106

Authors

Wali Haider Shaanxi Normal University
Hüseyin Budak Kocaeli University
Asia Shehzadi Central South University
Muhammad Toseef Nanjing University of Posts and Telecommunications

DOI:

https://doi.org/10.14244/lajm.v5i1.106

Keywords:

Inequalities of Boole’s rule, error bound, twice differentiable convex function

Abstract

This study investigates the error bounds associated with Boole's formula, a well-known open Newton--Cotes technique. By focusing on twice differentiable functions, a novel identity for Boole's formula is established. Establishing a new identity is a challenging task in this research because suitable kernels need to be found by replacing unknown values. The number of equations is greater than the number of unknowns, so the system has infinitely many solutions, and only one is suitable for Boole's type identity. Using the newly established equality, several Boole's type inequalities for twice differentiable convex functions are demonstrated. It offers significant advancements in the domain of computational mathematics and its applications. Additionally, numerical examples and graphical illustrations are included to validate the significance and applicability of these newly established inequalities.

Author Biographies

Wali Haider, Shaanxi Normal University

.

Hüseyin Budak, Kocaeli University

.

Asia Shehzadi, Central South University

.

Muhammad Toseef, Nanjing University of Posts and Telecommunications

.

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