MATEMATIKA FANIDA FOKKER–PLANK TENGLAMASINI ITERATIV USULDA SONLI YECHISH

Source abstract

This article studies the problem of iterative numerical solution of the Fokker– Planck equation, which describes the probability distribution of stochastic processes. The Fokker– Planck equation is of great importance in mathematical modeling of the time evolution of random processes in physical, technical, biological, economic and other complex systems. Due to the complexity of obtaining an analytical solution to the equation in many practical problems, there is a need to use finite difference and iterative calculation methods. In the study, the one- dimensional form of the Fokker–Planck equation was discretized in spatial coordinates and time, and an algorithm for determining its numerical solution was developed. During the calculation process, the change in the probability density function over time, the influence of drift and diffusion coefficients on the solution, and the stability conditions of the numerical scheme were analyzed. Using the iterative algorithm, new values of the probability density are calculated sequentially at each time step and the normalization condition is monitored. The results obtained show that the iterative method is effective and practically convenient in numerical modeling of the Fokker– Planck equation. The proposed approach can be used in modeling various stochastic systems, predicting probability distributions, and studying complex dynamic processes using computers.