The article investigates two approaches to the calculation of electric circuits in the conditions of uncertainty in the initial data or the influence of random influences, noise of different nature. The first approach is based on the application of interval and bilateral methods and is to some extent an example of robust methods. The second approach uses the stochastic Fokker-Planck equation and is the most informative. Although the application of the Fokker-Planck equation is limited by some conditions (random effects have the character of white noise or are subject to the Gaussian distribution law). This method has a wide scope of applicability. In turn, there are various methods for solving this differential equation. The article considers the solution of the corresponding problem using the finite difference method.
Examples of modeling of specific electrical and electronic circuits are given.
Арутюнян Р.В., Арутюнян Т.Р. Моделирование и методы расчета электрических цепей с приближёнными характеристиками. Математическое моделирование и численные методы, 2019, № 4, с. 50–68.
The purpose of the paper was to formulate and study the system of kinetic equations modeling the process of diffusion filtration based on a stochastic approach. Within the research we proved the theorem of existence and uniqueness of the solution with respect to the case of continuous density, obtained the solutions in uniformly convergent and asymptotic series and examined its behavior at infinity. Moreover, we considered the specific cases of density of the Delta-function type and uniform distribution. As a result, the finite-difference scheme for solving the corresponding Cauchy problem on finite time intervals is built and justified. The results of computer simulation are also given.
Arutyunyan R.V. Modeling of stochastic filtration processes in lattice systems. Mathematical Modeling and Computational Methods, 2017, №4 (16), pp. 17-30