Free Access
Issue
ESAIM: M2AN
Volume 32, Number 3, 1998
Page(s) 307 - 339
DOI https://doi.org/10.1051/m2an/1998320303071
Published online 27 January 2017
  1. M. ABRAHAMOWITZ & I. A. STEGUN Handbook of mathematematical functions. Dover Publications, INC, New York. [Google Scholar]
  2. V. V. ARISTOV & F. G. CHEREMISIN, 1980, The conservative splitting method for solving Boltzmann's equation. U.S.R.R. Comput. Maths. Math. Phys., Vol. 20, No. 1, p. 208-225. [MR: 564789] [Zbl: 0458.76061] [Google Scholar]
  3. A. A. ARSENEV & O. E. BURYAK, 1991, On the connection between a solution of the Boltzmann equation and a solution of the Landau-Fokker-Planck equation. Math. U.S.S.R. Sbornik, Vol. 69, No. 2, p. 465-478. [MR: 1055522] [Zbl: 0724.35090] [Google Scholar]
  4. A. A. ARSENEV & N. V. PESKOV, 1978, On the existence of a generalized solution of Landau's equation. U.S.S.R. Comput. Maths. Math. Phys., Vol. 17, p. 241-246. [MR: 470442] [Zbl: 0383.35064] [Google Scholar]
  5. Yu. A. BEREZIN, M. S. PEKKER & V. N. KUDICK, 1987, Conservative Finite-Difference Schemes for the Fokker-Planck Equation Not Violating the Low of an Increasing Entropy. Jour. of comp. phys., Vol. 69, p. 163-174. [MR: 892257] [Zbl: 0644.76091] [Google Scholar]
  6. R. L. BERGER, J. R. ALBRITTON, C. J. RANDALL, E. A. WILLIAMS, W. L. KRUER, A. B. LANGDON & C. J. HANNA, 1990, Stopping and thermahzation of interpenetrating plasma streams. Phys. Fluids B, Vol. 3, No. 1. [Google Scholar]
  7. A. V. BOBYLEV, 1981, Expansion of the Boltzmann collision integral in a Laudau series. Sov. Phys. Dolk., Vol. 20, No. 11, p. 740-742. [Google Scholar]
  8. A. V. BOBYLEV, I. F. POTAPENKO & V. A. CHUYANOV, Kinetic equations of the Landau type as a model of the Boltzmann equation and completely conservative difference schemes. U.S.R.R. Comput. Maths. Math. Phys., Vol. 20, No. 4, p. 190-201. [MR: 585294] [Zbl: 0493.76078] [Google Scholar]
  9. D. DECK & G. SAMBA, 1994, Le code Procions. Note CEA No. N 2780, CEA/CEL-V, F-94195 Villeneuve St. Georges Cedex. [Google Scholar]
  10. L. DESVILLETTES, 1992, On asymptotics of the Boltzmann equation when the collisions become grazing. Trans. Th. and Stat. Phys., Vol. 21, No. 3, p. 259-276. [MR: 1165528] [Zbl: 0769.76059] [Google Scholar]
  11. P. DEGOND & B. LUCQUIN-DESREUX, 1992, The Fokker-Plank assymptotics of the Boltzmann operator in the Coulomb case. Math. Mod. and Meth. in Appl. Sc., Vol. 2, No. 2, p. 167-182. [MR: 1167768] [Zbl: 0755.35091] [Google Scholar]
  12. P. DEGOND & B. LUCQUIN-DESREUX, 1994, An entropy scheme for the Fokker-Planck collision operator of plasma kinetic theory. Numer. Math., Vol. 68, p. 239-262. [MR: 1283340] [Zbl: 0806.65133] [Google Scholar]
  13. I. S. GRADSHTEYN & I. M. RYZHIK, Table of integrals, series and products. Academic press. [MR: 1773820] [Zbl: 0918.65002] [Google Scholar]
  14. N. A. KRALL & A. W. TRIVELPIECE, 1973, Principles of plasma physics. Mc Graw Hill book company. [Google Scholar]
  15. S. JORNA & L. WOOD, 1987, Fokker-Planck calculations on relaxation of anisotropic velocity distributions in plasmas. Phys. rev. A, Vol. 36, No. 1. [Google Scholar]
  16. O. LARROCHE, 1993, Kinetic simulation of a plasma collision experiment. Phys. Fluids B, Vol. 5, No. 8. [Google Scholar]
  17. M. LEMOU, C. BUET, S. CORDIER & P. DEGOND, A numerical, conservative and entropic scheme for the Fokker-Planck equation. In preparation. [Zbl: 0880.65112] [Google Scholar]
  18. B. LUCQUIN-DESREUX, 1992, Discrétisation de l'opérateur de Fokker-Planck dans le cas homogène. C. R. Acad. Sci., Paris, t. 314, p. 407-411. [MR: 1153725] [Zbl: 0749.35034] [Google Scholar]
  19. W. M. MAC DONALD, M. N. ROSENBLUTH & W. CHUCK, 1957, Relaxation of a system of particles with Coulomb interactions. Phys. Rev., Vol. 107, No. 2. [MR: 87304] [Zbl: 0085.44701] [Google Scholar]
  20. M. S. PEKKER & V. N. KUDICK, 1984, Conservative Difference Schemes for the Fokker-Planck Equation. U.S.R.R. Comput. Maths. Math. Phys., Vol. 24, No. 3, p. 206-210. [MR: 750108] [Google Scholar]
  21. I. F. POTAPENKO & V. A. CHUYANOV, 1979, A completely conservative difference scheme for the two-dimensional Landau equation. U.S.R.R. Comput. Math. Math. Phys., Vol. 20, No. 2, p. 249-253. [MR: 572407] [Google Scholar]
  22. J. C. WITNEY, 1970, Finite Difference Methods for the Fokker-Planck Equation. J. Comp. Phys., Vol. 6, p. 483-509. [MR: 273833] [Zbl: 0203.48501] [Google Scholar]

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