About modelling nonpolynomial integro-differential approximations

In this article the modelling of the nonpolynomial integro-differential splines is discussed. This splines interpolate function and its derivatives in knots of a grid and provide concurrence of integral size from approximated function and size of integral from spline on the set interval. Here explosive, continuous, and continuously differentiated several times basic splines are constructed. They allow to solve problems of the construction of approximation if we know the values of the function and its derivatives in knots of a grid and in the additional assumption that values of integrals from approached function on net intervals are known. Estimations errors are resulted and examples of splines are given.