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

On Fully Discrete Schemes for the Fermi Pencil-beam Equation

We consider a Fermi pencil beam model in two space dimensions (x; y), where x is aligned with the beam's penetration direction and y together with the scaled angular variable z, correspond to a bounded symmetric , transversal cross section. We study some fully discrete numerical schemes using the standard Galerkin and streamline diiusion nite element methods for discretization of the transversa...

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...

Characteristic Methods for Fokker-Planck and Fermi Pencil Beam Equations

The streamline diffusion method with implicit integration for the multi-dimensional Fermi Pencil Beam equation

We derive error estimates in the appropriate norms, for the streamlinediffusion (SD) finite element methods for steady state, energy dependent,Fermi equation in three space dimensions. These estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.High order SD method together with implicit integration are used. The formulationis strongly consistent...

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.