AN OPEN-TYPE GENERALIZED QUADRATURE RULE USING THE ANTI-GAUSSIAN APPROACH FOR NUMERICAL INTEGRATION

Abstract

We propose an open-type Generalized Quadrature Rule by combining the Anti-Gauss 3-point rule with Simpson's 3/8 rule. The convergence properties of the new rule are rigorously analysed, and error estimates confirm its superior accuracy compared to the individual base rules. To validate these findings, we apply the rule to a range of test integrals. The results highlight the Generalized Quadrature Rule's improved performance and dominance over its constituents, particularly in handling indefinite integrals, making it a valuable tool for practical applications.