In this paper, we apply spline quasi-interpolating operators on a bounded interval to solve numerically linear Fredholm integral equations of second kind by using superconvergent Nyström and degenerate kernel methods introduced in [4]. We give convergence orders associated with approximate solutions and their iterated versions in terms of spline quasi-interpolating order. Moreover, asymptotic expansions at the node/partition points for second kind Fredholm integral equations with Green’s type kernel are obtained in the Nyström method based on quadratic and cubic quasi-interpolants. Therefore, the Richardson extrapolation technique is used to improve the convergence orders. Finally, numerical examples and comparison with existing methods are given to illustrate the theoretical results and to show that the proposed methods improve the convergence orders.

在本文中，我们使用有界区间上的样条拟插值算子，通过使用超收敛Nyström和简并核方法[4]引入第二类数值线性Fredholm积分方程。我们根据样条拟插值顺序给出与近似解及其迭代版本相关的收敛顺序。此外，在Nyström方法的基础上，基于二次和三次拟插值，获得了带有格林型核的第二类Fredholm积分方程在节点/分区点处的渐近展开。因此，使用理查森外推技术来提高收敛阶数。最后，