A NOVEL QUADRATURE RULE FOR INTEGRATION OF ANALYTIC FUNCTIONS

This paper introduces a novel quadrature rule of precision 5 designed for the numerical integration of definite integrals involving analytic functions. The proposed method synergistically combines Simpson’s 1/3 rd rule with a quadrature rule derived from Hermite interpolation of degree 3. By harnessing the strengths of both techniques, we establish a new quadrature rule that delivers superior precision, thereby ensuring enhanced accuracy in integration tasks. The theoretical framework underpinning the new rule is developed, and we provide a comprehensive analysis of its convergence properties. Numerical experiments demonstrate the superior performance of the proposed method in comparison to traditional quadrature techniques. The results reveal significant improvements in accuracy and efficiency when applied to various classes of analytic functions. This work aims to advance numerical integration strategies and demonstrates the valuable potential of hybrid methods in enhancing computational performance for the integration of analytic functions.