Solution of the Four Dimensional Fokker-Planck Equation: Still a Challenge

نویسنده

  • A. Masud
چکیده

The accurate prediction of the response of a dynamical system is a necessary first step toward its design and eventual control. Development of high fidelity models of the system and excitation processes provides the means to accurately determine system response, assess the adequacy of the system in terms of its performance and safety, and suggest remedial action. However, a degree of uncertainty exists in the properties of nearly every physical system, as well as in most excitations. Thus, the predicted responses, at some scale, will contain some randomness, and the complete and accurate determination of these responses is a nontrivial matter. Here, we discuss the problems inherent in the analysis of a particular class of systems using the finite element method to solve related Fokker-Planck equations.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Pseudo-spectral ‎M‎atrix and Normalized Grunwald Approximation for Numerical Solution of Time Fractional Fokker-Planck Equation

This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.

متن کامل

Numerical Studies and Simulation of the Lower Hybrid Waves Current Drive by using Fokker – Planck Equation in NSST and HT-7 Tokamaks

Recent experiments on the spherical tokamak have discovered the conditions to create a powerful plasma and ensure easy shaping and amplification of stability, high bootstrap current and confinement energy. The spherical tours (ST) fusion energy development path is complementary to the tokamak burning plasma experiment such as NSTX and higher toroidal beta regimes and improves the design of a po...

متن کامل

Fokker–Planck approximation of the master equation in molecular biology

The master equation of chemical reactions is solved by first approximating it by the Fokker–Planck equation. Then this equation is discretized in the state space and time by a finite volume method. The difference between the solution of the master equation and the discretized Fokker–Planck equation is analyzed. The solution of the Fokker–Planck equation is compared to the solution of the master...

متن کامل

- ph / 9 80 70 09 v 2 1 2 Ju l 1 99 8 The Exact Solution of the Cauchy Problem for a generalized ” linear ” vectorial Fokker - Planck Equation - Algebraic Approach

The exact solution of the Cauchy problem for a generalized ”linear” vectorial Fokker-Planck equation is found using the disentangling techniques of R. Feynman and algebraic (operational) methods. This approach may be considered as a generalization of the Masuo Suzuki’s method for solving the 1-dimensional linear Fokker-Planck equation.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005