Integro sextic spline interpolation and its super convergence

In this paper, we use sextic B-splines to construct an approximating function based on the integral values, rather than the usual function values at the knots. It is called integro sextic spline interpolation. The super convergence (eighth, sixth and fourth order, respectively) in approximating function values, second-order derivative values and fourth-order derivative values at the knots is mainly proved.