Mathematical modeling of bending of a circular plate using $S$-splines

This article is dedicated to the use of higher degree $S$-splines for solving equations of the elasticity theory. As an example we consider the solution to the equation of bending of a plate on a circle. $S$-spline is apiecewise-polynomial function. Its coefficients are defined by two conditions. The first part of the coefficients are defined by the smoothness of the spline. The rest are determined using the least-squares method. We consider class $\mathbf{C}^4$ 7th degree $S$-splines.