Estimating the error of Gaussian quadratures with simple and multiple nodes by using their extensions with multiple nodes (Q285297)

A posteriori error estimates are a widely used technique in the theory of partial differential equations. Here the readers may refer to \textit{P. A. Farrell} et al. [Robust computational techniques for boundary layers. Boca Raton, FL: Chapman \& Hall/ CRC Press (2000; Zbl 0964.65083)]. In this manuscript, the authors suggest to employ it for estimating the error of the Gaussian quadratures. In particular, optimal alternatives to Gauss-Kronrod quadratures are suggested. A posteriori error estimates of Volterra integral equations of the first kind with discontinuous kernels solutions are used by \textit{D. Sidorov} [Integral dynamical models. Singularities, signals and control. Hackensack, NJ: World Scientific (2015; Zbl 1311.45012)].