Pencil-beam approximation of fractional Fokker-Planck

Characteristic Methods for Fokker-Planck and Fermi Pencil Beam Equations

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.

On the accuracy of the Fokker-Planck and Fermi pencil beam equations for charged particle transport.

Electron beam dose calculations are often based on pencil beam formulas such as the Fermi-Eyges formula. The Fermi-Eyges formula gives an exact solution of the Fermi equation. The Fermi equation can be derived from a more fundamental mathematical model, the linear Boltzmann equation, in two steps. First, the linear Boltzmann equation is approximated by the Fokker-Planck equation. Second, the Fo...

Parameters of the fractional Fokker-Planck equation

We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavytailed increments, and the transition probability density of the noise generating process. Explicit expressions for these parameters are derived both for finite and infinite variance of the rescaled transition probability de...

A Posteriori Error Estimates for the Fokker-planck and Fermi Pencil Beam Equations

We prove a posteriori error estimates for a nite element method for steady-state, energy dependent, Fokker-Planck and Fermi pencil beam equations in two space dimensions and with a forward-peaked scattering (i.e., with velocities varying within the right unit semicircle). Our estimates are based on a transversal symmetry assumption, together with a strong stability estimate for an associated du...