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Original Articles

Two alternative methods for solving the Vlasov Fokker–Planck equation

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Pages 951-957 | Received 20 Jan 2006, Accepted 17 Nov 2006, Published online: 26 Mar 2007

References

  • Chandrasekhar , S. 1943 . Stochastic problems in physics and astronomy . Reviews of Modern Physics , 15 : 1 – 89 .
  • Kramers , H. A. 1940 . Brownian motion in a field of force and the diffusion model of chemical reactions . Physica , 7 : 284 – 304 .
  • Risken , H. 1989 . The Fokker-Planck Equation , Berlin : Springer-Verlag .
  • Fokker , A. 1914 . The median energy of rotating electrical dipoles in radiation fields . Annalen Der Physik , 43 : 810 – 820 .
  • Liboff , R. L. 1969 . Introduction to the Theory of Kinetic Equations , New York : John Wiley .
  • Gardiner , C. W. 1985 . Handbook of Stochastic Methods , Berlin : Springer-Verlag .
  • Van Kampen , N. G. 1981 . Stochastic Processes in Physics and Chemistry , Amsterdam : North Holland .
  • Lebowitz , J. L. , Frisch , A. K. and Helefand , D. 1960 . Nonequilibrium distribution functions in a fluid . Physics of Fluids , 3 : 325 – 338 .
  • El-Wakil , S. A. , Elhanbaly , A. and Abdou , M. A. 2003 . Maximum entropy method for solving the collisional Vlasov equation . Physica A , 323 : 213 – 228 .
  • Beals , R. and Protopopescu , V. 1983 . On the asymptotic equivalence of the Fokker-Planck and diffusion equations . Transport Theory and Statistical. Physics , 12 : 109 – 127 .
  • Elhanbaly , A. and Abdou , M. A. 2006 . New application of Adomian decomposition method on Fokker Planck equation . Applied Mathematics and Computation , 182 : 301 – 312 .
  • Shtelen , W. M. and Stogny , V. I. 1989 . Symmetry properties of one- and two-dimensional Fokker-Planck equations . Journal of Physics A: Mathematical and General , 22 : L539 – L543 .
  • Burschka , M. A. and Titulear , U. M.J. 1981 . The kinetic boundary layer for the Fokker-Planck equation with absorbing boundary . Journal of Statistical Physics , 25 : 569 – 582 .
  • El-Wakil , S. A. , Elhanbaly , A. and Abdou , M. A. 1999 . On the diffusion-convection-reaction equations . Physica Scripta , 60 : 207 – 210 .
  • Weiss , G. H. and Gitterman , M. 1995 . Expansion of moments of the Smoluchowski equation . Physical Review E , 51 : 122 – 125 .
  • Ganapol , B. D. 1986 . Solution of the one group time dependent neutron transport equation in an infinite medium by polynomial reconstruction . Nuclear Science and Engineering , 92 : 272 – 279 .
  • El-Wakil , S. A. , Zahran , M. A. and Abdou , M. A. 2003 . The operator method for solving the fractional Fokker-Planck equation . Journal of Quantitative Spectroscopy and Radiative Transfer , 77 : 317 – 327 .
  • Suzuki , M. 1983 . New unified formulation of transient phenomena near the instability point on the basis of the fokker-planck equation . Physica A , 117 : 103 – 108 .
  • Suzuki , M. 1990 . Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations . Physics Letters A , 146 : 319 – 323 .
  • Suzuki , M. 1991 . General theory of fractal path integrals with applications to many-body theories and statistical physics . Journal of Mathematical Physics , 32 : 400 – 407 .
  • Suzuki , M. 1976 . Scaling theory of non-equilibrium systems near the instability point. I: General aspects of transient phenomena . Progress of Theoretical Physics , 56 : 77 – 94 .
  • Mickens , R. E. 1987 . Difference Equations , New York : Van Nostrand Reinhold .
  • Ming , C. F. , Fu-Ming and Fang , Fu-Kang . 1987 . The operator method for solving the moment equation of Fokker Planck equation . Communications in Theoretical Physics , 7 : 187

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