Numerical solution of the Fokker Planck equation for the probability density function of a stochastic process by traditional finite difference or finite element methods produces erroneous oscillations and negative values whenever the drift is large compared to the diffusion. Upwinding schemes to eli
Numerical solution of the Fokker-Planck equation with a dc electric field
β Scribed by I.P. Shkarofsky; M.M. Shoucri; V. Fuchs
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 1004 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0010-4655
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β¦ Synopsis
Using the IMSL package TWODEPEP, the full non-relativistic Fokker-Planck equation is solved numerically for the runaway electron distribution function in the presence of a dc electric field. A set of partial integro-differential equations derived from a Legendre expansion of the Fokker-Planck equation is solved simultaneously for the electron distribution parts up to f 3 with .10 non-Maxwellian and including the full electron-electron collision operator. The runaway distribution function and its moments yielding the non-linear conductivity, runaway rate, temperature and drift velocity are presented.
π SIMILAR VOLUMES
A new approach for the accurate numerical solution of the Fokker-Planck-Landau (FPL) equation in the nonhomogeneous case is presented. The method couples, through a time-splitting algorithm, a finite-volume scheme for the transport with a fast spectral solver for the efficient solution of the collis
## Abstract The paper considers the solution of the FokkerβPlanckβKolmogorov equation by the finite element method (FEM). The problem is set in a variational formulation suitable for the FEM. Some theoretical aspects related to applying the method are discussed. Discretization of the problem is car