Research Article

Advancing Numerical Evaluation of Cauchy Principal Value Integrals Using a Mixed Quadrature Rule

Abstract

In this Paper, a new derivative-based quadrature rule designed for evaluating complex Cauchy principal value integrals that posses’ singularities within the integration domain. A new quadrature rule has been constructed by modifying Simpson’s rule on the basis of Cauchy principal value. Further We utilize Cubic Hermite Interpolation to construct a quadrature rule. Both rules are of precision degree 4, which is reflected in the error analysis. Furthermore by utilizing the error associated with the two rules, a combined rule of degree of precision 6 has been developed. This new rule yields lower errors compared to the other rules while maintaining minimal runtime, as verified using several test integrals.