A METHOD OF PIECE-QUADRATIC INTERPOLATION OF A TABLED FUNCTION WITH A CONTINUOUS FIRST DERIVATIVE BASED ON LINEAR COMBINATION OF CENTRAL-SYMMETRIC PARABOLAS

Abstract

In engineering practice, one often has to deal with reference and experimental data, in particular, with tabularly specified functional dependencies. Such functions characterize the properties of materials, as well as physical and technical objects. The dielectric properties of materials are represented by functional dependences of the electric polarization of a substance or electric displacement on the strength of the electric field. Such functions are called polarization curves of dielectrics. Their significant nonlinearity is manifested in ferroelectrics. The magnetic properties of materials are represented by functional dependences of the magnetization of a substance or magnetic induction on the strength of the magnetic field. Such functions are called magnetization curves. Their essential nonlinearity is manifested in ferro- and ferrimagnets. The properties of technical objects are largely determined by the properties of materials, designs, geometric dimensions of parts, elements and assemblies. Information about the properties of standardized materials and products from them can be contained in reference books in graphical or tabular form in cases of non-linearity of the corresponding functional dependencies. In the course of technical calculations, they need to be smoothly interpolated. A method of piecewise-quadratic interpolation of a tabularly given function with a continuous first derivative is proposed based on the linear combination of modified (centrally symmetric) parabolas, which does not require the use of logical operations in calculations to determine a partial segment of the grid of argument values. A method for weighted minimization of the oscillatory effect for non-uniform grids of argument values is proposed. Computational experiments with the reference main magnetization curve of electrical steel show the high numerical stability of the proposed method with respect to the effect of oscillation and the technical flexibility in its application for solving practical problems of processing tabularly specified functional dependencies on essentially non-uniform grids of argument values, including those with a small number of tabular points.