Approximate solution of the Fokker-Planck-Kolmogorov equation

1995 ◽  
Vol 47 (3) ◽  
pp. 408-419 ◽  
Author(s):  
Yu. A. Mitropol'skii
Keyword(s):  
Approximate Solution ◽  
Kolmogorov Equation ◽  
Fokker Planck

Approximate solution of the Fokker-Planck-Kolmogorov equation by finite elements

1994 ◽  
Vol 10 (10) ◽  
pp. 763-771 ◽  
Author(s):  
Mohamed A. El-Gebeily ◽  
Hosam E. Emara Shabaik
Keyword(s):  
Approximate Solution ◽  
Finite Elements ◽  
Kolmogorov Equation ◽  
Fokker Planck

Approximate solution of the Fokker–Planck–Kolmogorov equation

2002 ◽  
Vol 17 (4) ◽  
pp. 369-384 ◽  
Author(s):  
M. Di Paola ◽  
A. Sofi
Keyword(s):  
Approximate Solution ◽  
Kolmogorov Equation ◽  
Fokker Planck

A class of nonlinear oscillational systems admitting exact solution of the Fokker-Planck-Kolmogorov equation

1991 ◽  
Vol 43 (10) ◽  
pp. 1282-1286
Author(s):  
Yu. A. Mitropol'skii ◽  
Nguen Tien Kkhiem
Keyword(s):  
Exact Solution ◽  
Kolmogorov Equation ◽  
Fokker Planck

A New Numerical Method for Solving Nonlinear Fractional Fokker–Planck Differential Equations

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
BeiBei Guo ◽  
Wei Jiang ◽  
ChiPing Zhang
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Reproducing Kernel ◽  
Numerical Solutions ◽  
Simple Algorithm ◽  
High Accuracy ◽  
Computational Work ◽  
Reproducing Kernel Theory ◽  
Transport Problems ◽  
Fokker Planck

The nonlinear fractional-order Fokker–Planck differential equations have been used in many physical transport problems which take place under the influence of an external force filed. Therefore, high-accuracy numerical solutions are always needed. In this article, reproducing kernel theory is used to solve a class of nonlinear fractional Fokker–Planck differential equations. The main characteristic of this approach is that it induces a simple algorithm to get the approximate solution of the equation. At the same time, an effective method for obtaining the approximate solution is established. In addition, some numerical examples are given to demonstrate that our method has lesser computational work and higher precision.

On uniqueness of probability solutions to the Fokker-Planck-Kolmogorov equation

2021 ◽  
Vol 212 (6) ◽  
Author(s):  
Vladimir Igorevich Bogachev ◽  
Tikhon Il'ich Krasovitskii ◽  
Stanislav Valer'evich Shaposhnikov
Keyword(s):  
Kolmogorov Equation ◽  
Fokker Planck

Model for the Suspensions Separation Process in Hydrodynamic Filters with a Rotating Filter Element

2021 ◽  
pp. 48-56
Author(s):  
Vladimir Devisilov ◽  
V. Lvov ◽  
E. Sharay
Keyword(s):  
Theoretical Calculation ◽  
Statistical Method ◽  
Separation Process ◽  
Filter Element ◽  
Kolmogorov Equation ◽  
Diffusion Type ◽  
Self Cleaning ◽  
Fokker Planck

The possibility of applying the probabilistic-statistical method for theoretical calculation of characteristics related to suspensions separation in self-cleaning hydrodynamic filters with a rotating filter element has been demonstrated. It has been shown that the change in characteristics of the suspensions separation in hydrodynamic filters with a rotating filter element can be satisfactorily described based on equations of diffusion type, in particular, using the Fokker–Planck–Kolmogorov equation. The main parameters of the separation process in hydrodynamic filters with a rotating filter element have been determined.

Approximate Solution of the Fokker–Planck Equation for a Multidegree of Freedom Frictionally Damped Bladed Disk Under Random Excitation

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Alwin Förster ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Approximate Solution ◽  
Weighting Function ◽  
Gaussian White Noise ◽  
Planck Equation ◽  
Random Excitation ◽  
Stationary Response ◽  
Bladed Disk ◽  
Fokker Planck Equation ◽  
Finite Differences Method ◽  
Fokker Planck

Bladed disks are subjected to different types of excitations, which cannot, in any, case be described in a deterministic manner. Fuzzy factors, such as slightly varying airflow or density fluctuation, can lead to an uncertain excitation in terms of amplitude and frequency, which has to be described by random variables. The computation of frictionally damped blades under random excitation becomes highly complex due to the presence of nonlinearities. Only a few publications are dedicated to this particular problem. Most of these deal with systems of only one or two degrees-of-freedom (DOFs) and use computational expensive methods, like finite element method or finite differences method (FDM), to solve the determining differential equation. The stochastic stationary response of a mechanical system is characterized by the joint probability density function (JPDF), which is driven by the Fokker–Planck equation (FPE). Exact stationary solutions of the FPE only exist for a few classes of mechanical systems. This paper presents the application of a semi-analytical Galerkin-type method to a frictionally damped bladed disk under influence of Gaussian white noise (GWN) excitation in order to calculate its stationary response. One of the main difficulties is the selection of a proper initial approximate solution, which is applicable as a weighting function. Comparing the presented results with those from the FDM, Monte–Carlo simulation (MCS) as well as analytical solutions proves the applicability of the methodology.

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