Finite Difference Value in Forming One-Dimensional Geometric Images Represented by Numerical Sequences of Elementary Functional Dependences

Abstract

Discrete modeling of continuous images by the static-geometric method in most cases is associated with certain errors. Therefore, it is relevant to study the formation of geometric images with a given accuracy, using a minimum amount of initial information. This will allow to create models with optimal discretization.
 Further development of this modeling method with rational decrease in initial information volume, is topical. The proposed line of research will open up new possibilities for its use in various industries, such as construction, engineering, economics etc.
 One of the objectives of this work is to continue research on the formation of discrete images of curved lines. The study is based on the classical finite difference method, static-geometric modeling method and the geometric apparatus of superpositions.
 The article proposes a method for determining the distribution functions of finite-difference values in the formation of discrete analogues of linear-fractional, exponential and hyperbolic functional dependencies using finite differences of different orders. These studies define a general method for obtaining similar patterns of distribution of the finite difference value in formation of discrete analogues of elementary functional dependencies using finite differences of different orders.
 Establishing a correspondence between the equation of the curve and the distribution function of a finite difference value can be the basis for assessing the accuracy of the formation of discrete frameworks of curves described by elementary functional dependencies.
 In the future, the results of this work will make it possible to determine coordinates of any point of a numerical sequence of the nth order and numerical sequences of elementary functional dependencies as a superposition of the coordinates of adjacent points. It can also be a superposition of arbitrarily given nodal points of these sequences, if the value of the final difference or its distribution function are already known.