A simple method for constructing integro spline quasi-interpolants

In this paper, we study a new method for function approximation from the given integral values over successive subintervals by using cubic B-splines. The method does not need any additional end conditions and it is easy to be implemented without solving any system of linear equations. The method is able to approximate the original function and its first and second-order derivatives over the global interval successfully. The approximation errors are well studied. Numerical results illustrate that our method is very effective.