Asymptotically Accurate Estimates of the Error for Exponentially Convergent Quadratures

Abstract: New asymptotically accurate estimates are made of the error in calculating quadratures. A procedure for extrapolating error is proposed that dramatically increases the accuracy of calculations. Many applied problems require highly precise and cost-efficient calculations of quadrature. In some cases that are important in practice, the quadratures of trapezoids and mean values yield not quadratic, but exponential convergence in the size of the grid step. © 2022, Allerton Press, Inc.