REGULARITIES OF VALUES CHANGE OF SUPERPOSITION COEFFICIENTS IN INTERPOLATION BY HYPERBOLIC FUNCTIONS

Abstract

In design of modern building structures, architectural coating forms, geometric design takes a significant place, when at a sketch stage basic geometric shapes are determined together with their advantages and disadvantages Using the geometric apparatus of superpositions in combination with the classical finite difference method we can significantly increase efficiency and expand capabilities of discrete modeling of geometric images.In particular, we can investigate the possibility of using as parabolic functional dependencies as any other ones as interpolants. Creating discrete modeling techniques, traditional interpolation methods do not allow using transcendental functions as interpolants. This is due to the fact that the system of transcendental equations, which is obtained by substituting initial conditions into these functions, cannot be solved in the general case. In this article it was investigated regularities of values change of superposition coefficients of three arbitrarily specified nodal points (both adjacent and non-adjacent) for discrete modeling of a catenary. These researches determine a general approach to obtaining similar regularities of values change of superposition coefficients of three arbitrary given nodal points (as adjacent as not-adjacent) to determine coordinates of n points of any modeled one-dimensional functional dependencies and arbitrary one-dimensional sets of points. The developed method allows transcendental curves to be drawn through specified points, which is not possible with usual interpolation methods. In the future, the results of this work will make it possible to determine regularities of change a value of one from three superposition coefficients for three given nodal points (as adjacent as not-adjacent) of various elementary functions. This will allow solving problems of continuous discrete interpolation and extrapolation by numerical sequences of any one-dimensional functional dependencies (to determine ordinates of desired points of discrete curves) without cumbersome operations of compiling and solving huge systems of linear and transcendental equations.