New error bounds for Boole's rule

TL;DR

This paper establishes new error bounds for Boole's rule, a numerical integration method, using computer-assisted proofs to enhance understanding of its accuracy.

Contribution

It provides the first novel error bounds for Boole's rule, extending the analysis of Newton-Cotes formulas beyond Simpson's rule.

Findings

New error bounds for Boole's rule derived

Computer-assisted proofs used for validation

Enhanced understanding of Boole's rule accuracy

Abstract

In recent years, a lot of research was devoted to Simpson's rule for numerical integration. In the paper we study a natural successor of Simpson's rule, namely the Boole's rule. It is the Newton-Cotes formula in the case where the interval of integration is divided into four subintervals of equal length. With computer software assistance, we prove novel error bounds for Boole's rule.