On the superconvergence of some quadratic integro-splines at the mid-knots of a uniform partition

In this paper, we illustrate some new superconvergence of four kinds of quadratic integro-splines. It is proved that these quadratic integro-splines possess superconvergence in function values approximation (fourth order convergent) and in second-order derivatives approximation (second order convergent) at the mid-knots of a uniform partition.