
A. N. Firsov, A. A. Zhilenkov, S. G. Chernyi Solving Problems in Transportation Systems Modeled by the Nonlinear KolmogorovFeller Equation 

Abstract.
The paper describes the construction of a solution to the KolmogorovFeller equation with a nonlinear drift coefficient. This and similar equations are used in problems of the theory of transport and diffusion. Equations of this type are found in stochastic problems of the theory of safety and reliability, the dynamics of stellar systems, and even in economic problems. The paper proposes a constructive method for solving the stationary KolmogorovFeller equation with a nonlinear drift coefficient. The corresponding algorithms are constructed and their convergence is justified. The basis of the proposed method is the application of the Fourier transform.
Keywords:
KolmogorovFeller equation; nonlinear drift coefficient; constructive method for solving.
PP. 8493.
DOI 10.14357/20718632210209 References
1. Tikhonov V.I., Mironov M.A. Markov processes. Moscow, Soviet radio, 1977. (in Russian) 2. Tikhonov V.I., Kharisov V.N. Statistic analysis and synthesis of radio devices and systems. Moscow, Radio and communication, 1991. (in Russian) 3. Aleksandrov V.D. Exact solution of the stationary KolmogorovFeller equation // Review of applied and industrial mathematics. 2002. vol. 9. i. 1. P. 106, (in Russian) 4. Artemyev V.M., Ivanovskyi A.V. Discrete control systems with a random quantization period. Moscow, Energoatomizdat, 1986. 458 p. (in Russian) 5. Fedoryuk M.V. Ordinary differential equations. Moscow, Nauka, 1980. 458 p. (in Russian) 6. Rudenko O.V., Dubkov A.A., Gurbatov S.N. On exact solutions of the Kolmogorov–Feller equation // Doklady Akademii nauk. 2016.vol. 469 (4). P.414418. 7. King I.R. An Introduction to Classical Stellar Dynamics. Berkeley: University of California, 1994. 8. Zhilenkov A., Chernyi S., Sokolov S., Nyrkov A., Intelligent autonomous navigation system for UAV in randomly changing environmental conditions // J. Intell. Fuzzy Syst. 2020. 1–7. doi:10.3233/jifs179741 9. Sokolov S., Zhilenkov, A., Chernyi, S., Nyrkov, A., & Mamunts, D. Dynamics Models of Synchronized Piecewise Linear Discrete Chaotic Systems of High Order // Symmetry. 2019. 11(2). 236. doi: 10.3390/sym11020236 10. Zhilenkov A.A., Chernyi S.G. Automatic estimation of defects in composite structures as disturbances based on machine learning classifiers oriented mathematical models with uncertainties // Journal of Information Technologies and Computing Systems. 2020. № 3. С. 1329.
