Method of interpolation using root-fractional-rational functions of different orders

The possibility of interpolating different kinds of mathematical functions using different order root-fractional-rational functions, namely, second, third, and fourth, is considered in the article. Generally, it is shown that root-fractional-rational functions are given a precision interpolation with a small value of error even for stiff analytical dependences. Root-fractional-rational functions from second to fourth order are considered, and corresponding analytical relations for defining polynomial coefficients in the nominator and the denominator are given. It is also proven that the number of necessary points for interpolation corresponds to the value 2n+1, where n is the order of the root-fractional-rational function. Examples of interpolation of different functions for electrodynamics problems, simulation of magnetic lenses, probability tasks, and fuzzy-logic tasks are given; the error of interpolation for all considered examples is also defined. All presumptions of theoretical analysis are tested and verified using the original elaborated computer software, created using the Python programming language means. In the most considered examples, the resulting error of interpolation is smaller than a few percent. The graphic results of testing the proposed method of interpolation are also given.