THE ONE-DIMENSIONAL GEOMETRIC IMAGES FORMATION BY SUPERPOSITIONS OF POINT SETS UNDER THE GIVEN BOUNDARY CONDITIONS AND FINITE DIFFERENCE

A variation of the external load distribution function between nodes of a discrete grid in the static-geometric method allows discretely modeling curves of different shapes and solving problems of discrete interpolation on the area. The form of the continuous analogue of the discretely presented curve directly depends on the nature of the functions specified control load, which forms the discretely presented curve (DPC). There are known studies of the aspects of the relationship between the static geometric method of forming the DPC and the analytical description of a continuous curve through the synthesis of the static geometric method of forming discrete curves and the method of modeling them with numerical sequences. Separate issues of determining the correspondence of the equations of the continuous surface to the discrete function of the distribution of the external load are also investigated. This article examines the patterns of changes in the values of the superposition coefficients of two arbitrarily specified, both adjacent and non-adjacent nodal points, under the condition of a known distribution law of the magnitude of the finite difference, which in some cases will be a prototype of the external load between the nodes of the frame, which is a discrete model of a defined geometric image. If we change the uniformly distributed value of the finite difference or the value of the distribution function of the value of the finite difference, or the ordinates of one or two (marginal) nodal points at fixed values of the superposition coefficients, we can control the shape of the curve, discretely represented by the nodal points of its numerical sequence. The research data determine a general approach to obtaining similar patterns of changes in the values of the superposition coefficients of two arbitrarily specified, both adjacent and non-adjacent nodal points for determining the coordinates of points of modeling any one-dimensional functional dependencies and arbitrary one-dimensional sets of points. The results of the study of the regularities of changes in the values of the superposition coefficients given by two nodal points of different elementary functions, under the condition of a known distribution law of the magnitude of the finite difference, will allow solving the problems of continuous discrete interpolation and extrapolation by numerical sequences of any one-dimensional functional dependencies (determine the ordinates of the sought points of discrete curves) without time-consuming operations of assembling and solving large systems of linear equations