Application of twice continuously differentiable S-spline

This article is dedicated to an application of 5th order smoothing S-splines. Such splines are piece-wise polynomial functions. First three coefficients are defined by condition of smoothing of 2nd order, while another three coefficients - by method of minimal quads. These splines are used for building of a 6th order quadrature formulas. Also, here is presented a method and example of solving of Puasson's equation for simply connected domain by using these splines. Corresponding estimations are also given.