Comparison of Gauss Quadrature and Newton–Cotes methods of order 10 in definite integral calculations

Abstract

This study aims to evaluate and compare the accuracy of the Gauss Quadrature Method and the 10th Order Newton–Cotes Method based on numerical error in computing definite integrals, especially for complex functions that are difficult to solve analytically. The Gauss Quadrature Method studied includes the use of 2-point, 3-point, 4-point, 5-point, and 6-point rules, where the term points refers to the number of nodes used in the integration process. In contrast, the 10th-order Newton–Cotes Method is used for comparison, based on a high-degree interpolation polynomial at equidistant points. The comparison of the two methods is based on the accuracy of the numerical results as the main criterion. In this study, Microsoft Excel is used as a tool for numerical calculations. The results show that the Gauss Quadrature Method with 6 points provides numerical integral results with the highest level of accuracy compared to the Gauss Quadrature Method with fewer points, but generally produces larger errors than the 10th Order Newton–Cotes Method. These results indicate that, for the cases considered in this study, the 10th-order Newton–Cotes method is more efficient and accurate for calculating definite integrals.