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S Chen - One of the best experts on this subject based on the ideXlab platform.
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finite difference approximations for the fractional Fokker planck equation
Applied Mathematical Modelling, 2009Co-Authors: S Chen, P. ZhuangAbstract:The fractional Fokker–Planck equation has been used in many physical transport problems which take place under the influence of an external force field. In this paper we examine some practical numerical methods to solve a class of initial-boundary value problems for the fractional Fokker–Planck equation on a finite domain. The solvability, stability, consistency, and convergence of these methods are discussed. Their stability is proved by the energy method. Two numerical examples are also presented to evaluate these finite difference methods against the exact analytical solutions.
Anthony R. Bell - One of the best experts on this subject based on the ideXlab platform.
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A review of Vlasov-Fokker-Planck numerical modeling of inertial confinement fusion plasma
Journal of Computational Physics, 2012Co-Authors: Alexander Thomas, Michail Tzoufras, A. P. L. Robinson, Robert Kingham, Christopher Ridgers, Mark Sherlock, Anthony R. BellAbstract:The interaction of intense lasers with solid matter generates a hot plasma state that is well described by the Vlasov-Fokker-Planck equation. Accurate and efficient modeling of the physics in these scenarios is highly pertinent, because it relates to experimental campaigns to produce energy by inertial confinement fusion on facilities such as the National Ignition Facility. Calculations involving the Vlasov-Fokker-Planck equation are computationally intensive, but are crucial to proper understanding of a wide variety of physical effects and instabilities in inertial fusion plasmas. In this topical review, we will introduce the background physics related to Vlasov-Fokker-Planck simulation, and then proceed to describe results from numerical simulation of inertial fusion plasma in a pedagogical manner by discussing some key numerical algorithm developments that enabled the research to take place. A qualitative comparison of the techniques is also given.
Weihua Deng - One of the best experts on this subject based on the ideXlab platform.
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numerical algorithm for the time fractional Fokker planck equation
Journal of Computational Physics, 2007Co-Authors: Weihua DengAbstract:Anomalous diffusion is one of the most ubiquitous phenomena in nature, and it is present in a wide variety of physical situations, for instance, transport of fluid in porous media, diffusion of plasma, diffusion at liquid surfaces, etc. The fractional approach proved to be highly effective in a rich variety of scenarios such as continuous time random walk models, generalized Langevin equations, or the generalized master equation. To investigate the subdiffusion of anomalous diffusion, it would be useful to study a time fractional Fokker-Planck equation. In this paper, firstly the time fractional, the sense of Riemann-Liouville derivative, Fokker-Planck equation is transformed into a time fractional ordinary differential equation (FODE) in the sense of Caputo derivative by discretizing the spatial derivatives and using the properties of Riemann-Liouville derivative and Caputo derivative. Then combining the predictor-corrector approach with the method of lines, the algorithm is designed for numerically solving FODE with the numerical error O(k^m^i^n^{^1^+^2^@a^,^2^})+O(h^2), and the corresponding stability condition is got. The effectiveness of this numerical algorithm is evaluated by comparing its numerical results for @a=1.0 with the ones of directly discretizing classical Fokker-Planck equation, some numerical results for time fractional Fokker-Planck equation with several different fractional orders are demonstrated and compared with each other, moreover for @a=0.8 the convergent order in space is confirmed and the numerical results with different time step sizes are shown.
Laurent Thomann - One of the best experts on this subject based on the ideXlab platform.
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on global existence and trend to the equilibrium for the vlasov poisson Fokker planck system with exterior confining potential
Journal of Functional Analysis, 2016Co-Authors: Frederic Herau, Laurent ThomannAbstract:We prove a global existence result with initial data of low regularity, and prove the trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with small non linear term but with a possibly large exterior confining potential in dimension $d=2$ and $d=3$. The proof relies on a fixed point argument using sharp estimates (at short and long time scales) of the semi-group associated to the Fokker-Planck operator, which were obtained by the first author.
P. Zhuang - One of the best experts on this subject based on the ideXlab platform.
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finite difference approximations for the fractional Fokker planck equation
Applied Mathematical Modelling, 2009Co-Authors: S Chen, P. ZhuangAbstract:The fractional Fokker–Planck equation has been used in many physical transport problems which take place under the influence of an external force field. In this paper we examine some practical numerical methods to solve a class of initial-boundary value problems for the fractional Fokker–Planck equation on a finite domain. The solvability, stability, consistency, and convergence of these methods are discussed. Their stability is proved by the energy method. Two numerical examples are also presented to evaluate these finite difference methods against the exact analytical solutions.