A deterministic particle method for the Vlasov-Fokker-Planck equation in one dimension. (English) Zbl 1151.65073
The approximation of the Vlasov-Fokker-Planck equation is studied in one spatial dimension for the model of collisional electrostatic plasma. The equation is linear in that the electric field is given as a known function that is not internally consistent with the phase space distribution functcion. The approximation method applied is the authors’ deterministic particle method. Here the analysis of the stability and convergence of the numerical method is carried out. Computations done show the convergence of the numerical solution. As regards the long term asymptotics of the computed solution, it is in agreement with the steady state solution formerly given by F. Bouchet and J. Dolbeault [Differ. Integral Equ. 8, No. 3, 487–514 (1995; Zbl 0830.35129)].
Reviewer: Iván Abonyi (Budapest)
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
| 82D10 | Statistical mechanics of plasmas |
| 76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
| 78A35 | Motion of charged particles |
| 78M20 | Finite difference methods applied to problems in optics and electromagnetic theory |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
Keywords:
Vlasov-Fokker-Planck equation; deterministic particle method; numerical examples; finite difference methodCitations:
Zbl 0830.35129References:
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