Fredholm integral equations of the second kind that are defined on a finite or infinite interval arise in many applications. This paper discusses Nystr\"om methods based on Gauss quadrature rules for the solution of such integral equations. It is important to be able to estimate the error in the computed solution, because this allows the choice of an appropriate number of nodes in the Gauss quadrature rule used. This paper explores the application of averaged and weighted averaged Gauss quadrature rules for this purpose, and introduces new stability properties for them.

翻译：定义在有限或无限区间上的第二类Fredholm积分方程在许多应用中都会出现。本文讨论基于高斯求积规则的Nyström方法求解此类积分方程。能够估计计算解的误差非常重要，因为这有助于选择所使用的Gauss求积规则中的适当节点数。本文探讨了平均和加权平均高斯求积规则在此类问题中的应用，并引入了它们的新稳定性性质。