The Third Romberg Extrapolate as a Numerical Integration (British Journal of Multidisciplinary and Advanced Studies, 2025)
Modern techniques for quadrature include, but are not limited to, the Trapezium rule, the Midpoint rule, and Simpson’s rule. The accuracy of these methods can be improved by employing Romberg’s method. This is achieved by applying each method to a definite integral, subdividing it into multiple intervals, and then taking appropriate linear combinations of the resulting estimates to produce approximations with high-order accuracy. In this work, the third Romberg extrapolate is applied to a definite integral, and its solution is compared with the exact solution to demonstrate its accuracy.