Integro quadratic spline interpolation

In this paper, we use quadratic B-splines to reconstruct an approximating function by using the integral values of successive subintervals, rather than the usual function values at the knots. It is called integro quadratic spline interpolation. Compared to the other existing methods, our method can tackle integro interpolation problem from the integral values on arbitrary successive subintervals. The general approximation error is studied and the super convergence property is also derived when the interval is equally partitioned. Moreover, it can work successfully without any boundary condition. Numerical experiments show our method is easy to implement and effective.