Error Bounds of Boole's Formula for Twice Differentiable Convex Functions with Numerical Analysis
DOI:
https://doi.org/10.14244/lajm.v5i1.106Palavras-chave:
Inequalities of Boole’s rule, error bound, twice differentiable convex functionResumo
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.
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Copyright (c) 2026 Wali Haider, Hüseyin Budak, Asia Shehzadi, Muhammad Toseef
Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.
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