CALCULATION OF ELECTRIC POWER AND TEMPERATURE DISTRIBUTION IN AN ELECTRIC HEAT ACCUMULATING CONVERTER

Abstract

This paper presents a generalized approach to determining superposition coefficients for predefined layouts of two-dimensional point sets. The proposed approach provides the possibility of solving problems of continuous discrete interpolation and extrapolation by numerical sequences for arbitrary two-dimensional point sets using three preassigned nodal points.

The study is aimed at the further development of methods for modeling discrete geometric forms through the application of the classical finite difference method, the static-geometric approach, and the geometric apparatus of superpositions.

The research is based on the authors’ previous results devoted to identifying patterns in the variation of superposition coefficients of three nodal points of polynomial functions within selected computational schemes.

The paper investigates the process of forming discrete frameworks of two-dimensional geometric forms based on a known value of a recurrent relation with a specified uniform step in plan.

As a result, recurrent formulas were obtained for determining the values of the superposition coefficients of three nodal points of a given framework layout of a discrete geometric form. Under the condition of fixed values of the superposition parameters, different discrete frameworks may be formed on the basis of any computational scheme.

The obtained results make it possible to construct discrete geometric forms based on the coordinates of three given nodal points within a selected computational scheme.

The conducted research establishes a generalized approach to identifying patterns in the variation of superposition coefficients, which may be used to calculate the applicates of an arbitrary number of points in the modeling of arbitrary two-dimensional point sets.

Keywords: discrete modeling, static-geometric method, geometric apparatus of superpositions, recurrent relation value, superposition coefficients.