scholarly journals Modified Fokker-Planck Acceleration for Forward-Peaked Transport Problems in Slab Geometry

2021 ◽  
pp. 1-24
Author(s):  
J.J. Kuczek ◽  
J.K. Patel ◽  
R. Vasques
Keyword(s):  
Slab Geometry ◽  
Transport Problems ◽  
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.

Application of He’s Homotopy Perturbation Method for Solving Fractional Fokker-Planck Equations

2009 ◽  
Vol 64 (12) ◽  
pp. 788-794 ◽  
Author(s):  
Mohamed M. Mousa ◽  
Aidarkhan Kaltayev
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Planck Equation ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Homotopy Perturbation ◽  
External Force Field ◽  
Promising Tool ◽  
Transport Problems ◽  
Fokker Planck

Abstract The fractional Fokker-Planck equation (FFPE) has been used in many physical transport problems which take place under the influence of an external force field and other important applications in various areas of engineering and physics. In this paper, by means of the homotopy perturbation method (HPM), exact and approximate solutions are obtained for two classes of the FFPE initial value problems. The method gives an analytic solution in the form of a convergent series with easily computed components. The obtained results show that the HPM is easy to implement, accurate and reliable for solving FFPEs. The method introduces a promising tool for solving other types of differential equation with fractional order derivatives

Analytical methods for computational modeling of fixed-source slab-geometry discrete ordinates transport problems: Response matrix and hybrid SN

2013 ◽  
Vol 69 ◽  
pp. 77-84 ◽  
Author(s):  
Davi M. Silva ◽  
Emílio J. Lydia ◽  
Mateus R. Guida ◽  
José H. Zani ◽  
Hermes Alves Filho ◽  
...  
Keyword(s):  
Computational Modeling ◽  
Analytical Methods ◽  
Discrete Ordinates ◽  
Response Matrix ◽  
Slab Geometry ◽  
Transport Problems
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