THE FRACTAL FUNCTION APPROXIMATION AND ITS APPLICATION TO AERODYNAMIC MODELING

The fractal function approximation is an important branch of fractal theory. Compared with the ordinary function approximation, its advantage is that it can not only improve the accuracy of the approximation, but also maintain the fractional-dimensional characteristics of the objective function. However, in the process of studying the fractal function approximation, it is inevitable to calculate the fractal dimension of the sum function after adding multiple functions. This paper systematically sorts out and computes the fractal dimension of sum functions for different cases, so as to make a good theoretical foundation for fractal function approximation. Finally, considering that the change of aircraft aerodynamic value has fractional dimension characteristics, the use of the fractional function to approximate the aerodynamic numerical function has an inherent advantage, and the use of fractional calculus for aerodynamic modeling can more accurately measure the maximum angle of attack. Therefore, the application of fractional calculus and fractal function approximation theory in aerodynamic numerical modeling has been discussed in detail at the end of this paper, and the corresponding fractional aerodynamic modeling process is also demonstrated.