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Volumn 36, Issue 3, 1999, Pages 953-973

Numerical analysis of conservative and entropy schemes for the Fokker-Planck-Landau equation

Author keywords

Cauchy problem; Fokker Planck Landau equation; Kinetic models; Numerical schemes; System of ordinary differential equations

Indexed keywords


EID: 0000449286     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142997322102     Document Type: Article
Times cited : (30)

References (30)
  • 1
    • 0000062470 scopus 로고
    • On the connection between a solution of the Boltzmann equation and a solution of the Landau-Fokker-Planck equation
    • A.A. ARSENE'V AND O.E. BURYAC, On the connection between a solution of the Boltzmann equation and a solution of the Landau-Fokker-Planck equation, Math. USSR Sbornik, 69 (1991), pp. 465-478.
    • (1991) Math. USSR Sbornik , vol.69 , pp. 465-478
    • Arsene'v, A.A.1    Buryac, O.E.2
  • 2
    • 0011004948 scopus 로고
    • On the existence of a generalized solution of Landau's equation
    • A.A. ARSENE'V AND N.V. PESKOV, On the existence of a generalized solution of Landau's equation, USSR Comput. Math. Math. Phys., 17 (1977), pp. 241-246.
    • (1977) USSR Comput. Math. Math. Phys. , vol.17 , pp. 241-246
    • Arsene'v, A.A.1    Peskov, N.V.2
  • 3
    • 0001575743 scopus 로고
    • Conservative finite difference schemes for the Fokker-Planck equation not violating the law of an increasing entropy
    • YU.A. BEREZIN, V.N. KHUDICK, AND M.S. PEKKER, Conservative finite difference schemes for the Fokker-Planck equation not violating the law of an increasing entropy, J. Comput. Phys., 69 (1987), pp. 163-174.
    • (1987) J. Comput. Phys. , vol.69 , pp. 163-174
    • Berezin, Yu.A.1    Khudick, V.N.2    Pekker, M.S.3
  • 4
    • 0001288577 scopus 로고
    • On the generalization of the Boltzmann H-theorem for a spatially homogeneous Maxwell gas
    • A.V. BOBYLEV AND G. TOSCANI, On the generalization of the Boltzmann H-theorem for a spatially homogeneous Maxwell gas, J. Math. Phys., 33 (1992), p. 7.
    • (1992) J. Math. Phys. , vol.33 , pp. 7
    • Bobylev, A.V.1    Toscani, G.2
  • 5
    • 49149140237 scopus 로고
    • Kinetic equations of the Landau-type as a model of the Boltzmann equation and completely conservative difference schemes
    • A.V. BOBILEV, I.F. POTAPENKO, AND V.A. CHUYANOV, Kinetic equations of the Landau-type as a model of the Boltzmann equation and completely conservative difference schemes, U.S.S.R. Comput. Math. Math. Phys., 20, 4 (1981), pp. 190-201.
    • (1981) U.S.S.R. Comput. Math. Math. Phys. , vol.20 , Issue.4 , pp. 190-201
    • Bobilev, A.V.1    Potapenko, I.F.2    Chuyanov, V.A.3
  • 6
    • 85034151561 scopus 로고    scopus 로고
    • Numerical scheme for the spherical Fokker-Planck-Landau operator
    • preprint in L.A.N. (Paris 6) 97032, submitted
    • C. BUET AND S. CORDIER, Numerical Scheme for the Spherical Fokker-Planck-Landau operator, J. Comput. Phys., preprint in L.A.N. (Paris 6) 97032, 1997; submitted.
    • (1997) J. Comput. Phys.
    • Buet, C.1    Cordier, S.2
  • 7
    • 0031570220 scopus 로고    scopus 로고
    • Fast algorithms for numerical conservative and entropy approximations of the Fokker-Planck-Landau operator
    • C. BUET, S. CORDIER, P. DEGOND, AND M. LEMOU, Fast algorithms for numerical conservative and entropy approximations of the Fokker-Planck-Landau operator, J. Comput. Phys., 133 (1997), pp. 1036-1053.
    • (1997) J. Comput. Phys. , vol.133 , pp. 1036-1053
    • Buet, C.1    Cordier, S.2    Degond, P.3    Lemou, M.4
  • 8
    • 0001625099 scopus 로고
    • Numerical integration of the Fokker-Planck equation and the evolution of star clusters
    • H. COHN, Numerical integration of the Fokker-Planck equation and the evolution of star clusters, The Astrophysical Journal, 234 (1979), pp. 1036-1053.
    • (1979) The Astrophysical Journal , vol.234 , pp. 1036-1053
    • Cohn, H.1
  • 9
    • 0000006668 scopus 로고
    • Late core collapse in star clusters and the gravothermal instability
    • H. COHN, Late core collapse in star clusters and the gravothermal instability, The Astrophysical Journal, 242 (1980), pp. 765-771.
    • (1980) The Astrophysical Journal , vol.242 , pp. 765-771
    • Cohn, H.1
  • 11
    • 0000583046 scopus 로고
    • The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case
    • P. DEGOND AND B. LUCQUIN-DESREUX, The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case, Math. Models Methods Appl. Sci., 2 (1992), pp. 167-182.
    • (1992) Math. Models Methods Appl. Sci. , vol.2 , pp. 167-182
    • Degond, P.1    Lucquin-Desreux, B.2
  • 12
    • 21344479554 scopus 로고
    • An entropy scheme for the Fokker-Planck collision of plasma kinetic theory
    • P. DEGOND AND B. LUCQUIN-DESREUX, An entropy scheme for the Fokker-Planck collision of plasma kinetic theory, Numer. Math., 68 (1994), pp. 239-262.
    • (1994) Numer. Math. , vol.68 , pp. 239-262
    • Degond, P.1    Lucquin-Desreux, B.2
  • 13
    • 84947512966 scopus 로고
    • On asymptotics of the Boltzmann equation when the collisions become grazing
    • L. DESVILLETTES, On asymptotics of the Boltzmann equation when the collisions become grazing, Transport Theory and Statist. Phys., 21 (1992), pp. 259-276.
    • (1992) Transport Theory and Statist. Phys. , vol.21 , pp. 259-276
    • Desvillettes, L.1
  • 17
    • 0039984514 scopus 로고    scopus 로고
    • On conservative and entropy discrete axisymmetric Fokker-Planck operators
    • E. FRENOD AND B. LUCQUIN-DESREUX, On conservative and entropy discrete axisymmetric Fokker-Planck operators, RAIRO Modél. Math. Anal. Numér., 33 (1998), pp. 307-339.
    • (1998) RAIRO Modél. Math. Anal. Numér. , vol.33 , pp. 307-339
    • Frenod, E.1    Lucquin-Desreux, B.2
  • 18
    • 0002207841 scopus 로고
    • Random discrete velocity method: Possible bridges between the Boltzmann equation, discrete velocity models and particle simulation?
    • Proceedings, Rapallo
    • R. ILLNER AND S. RJASANOW, Random discrete velocity method: possible bridges between the Boltzmann equation, discrete velocity models and particle simulation? Nonlinear Kinetic Theories and Mathematical Aspects of Hyperbolic Systems, in Proceedings, Rapallo, 1992.
    • (1992) Nonlinear Kinetic Theories and Mathematical Aspects of Hyperbolic Systems
    • Illner, R.1    Rjasanow, S.2
  • 19
    • 84941465845 scopus 로고
    • A lower bound for discrimination information interms of variation
    • S. KULLBACK, A lower bound for discrimination information interms of variation, IEEE Trans. Inform. Theory, 4 (1967), pp. 126-127.
    • (1967) IEEE Trans. Inform. Theory , vol.4 , pp. 126-127
    • Kullback, S.1
  • 20
    • 0001570756 scopus 로고
    • Kinetic simulations of a plasma collision experiment
    • O. LARROCHE, Kinetic simulations of a plasma collision experiment, Phys. Fluids B, 5 (1993), pp. 2816-2840.
    • (1993) Phys. Fluids B , vol.5 , pp. 2816-2840
    • Larroche, O.1
  • 21
    • 0001395574 scopus 로고
    • Exact solutions of the Fokker-Planck equation
    • M. LEMOU, Exact solutions of the Fokker-Planck equation, C. R. Acad. Sci. Paris Sér. I Math., 319 (1994), pp. 579-583.
    • (1994) C. R. Acad. Sci. Paris Sér. I Math. , vol.319 , pp. 579-583
    • Lemou, M.1
  • 22
    • 0032338331 scopus 로고    scopus 로고
    • Multipole expansions for the Fokker-Planck equation
    • M. LEMOU, Multipole expansions for the Fokker-Planck equation, Numer. Math., 78 (1998), pp. 597-618.
    • (1998) Numer. Math. , vol.78 , pp. 597-618
    • Lemou, M.1
  • 23
    • 0000311559 scopus 로고
    • An improved kinetic model for the polar outflow of a minor ion
    • O. LIE-SVENDSEN AND M.H. REES, An improved kinetic model for the polar outflow of a minor ion, J. Geophys. Res., (1995).
    • (1995) J. Geophys. Res.
    • Lie-Svendsen, O.1    Rees, M.H.2
  • 24
    • 0000719314 scopus 로고
    • Generation of solar wind proton tails and double beams by coulomb collisions
    • S. LIVI AND E. MARSCH, Generation of solar wind proton tails and double beams by coulomb collisions, J. Geophys. Res., 92 (1987), pp. 7255-7261.
    • (1987) J. Geophys. Res. , vol.92 , pp. 7255-7261
    • Livi, S.1    Marsch, E.2
  • 25
    • 0000045474 scopus 로고
    • Discrétisation de l'opérateur de Fokker-Planck dans le cas homogène
    • B. LUCQUIN-DESREUX, Discrétisation de l'opérateur de Fokker-Planck dans le cas homogène, C. R. Acad. Sci. Paris Sér. I Math., 314 (1992), pp. 407-411.
    • (1992) C. R. Acad. Sci. Paris Sér. I Math. , vol.314 , pp. 407-411
    • Lucquin-Desreux, B.1
  • 26
    • 0001425190 scopus 로고
    • Conservative difference schemes for the Fokker-Planck equation
    • M.S. PEKKER AND V.N. KHUDIK, Conservative difference schemes for the Fokker-Planck equation, U.S.S.R. Comput. Math. Math. Phys., 24 (1984), pp. 206-210.
    • (1984) U.S.S.R. Comput. Math. Math. Phys. , vol.24 , pp. 206-210
    • Pekker, M.S.1    Khudik, V.N.2
  • 27
    • 0000404135 scopus 로고
    • A completely conservative difference scheme for the two-dimensional Landau equation
    • I.F. POTAPENKO AND V.A. CHUYANOV, A completely conservative difference scheme for the two-dimensional Landau equation, U.S.S.R. Comput. Math. Math. Phys., 20 (1980), pp. 249-253.
    • (1980) U.S.S.R. Comput. Math. Math. Phys. , vol.20 , pp. 249-253
    • Potapenko, I.F.1    Chuyanov, V.A.2
  • 30
    • 0041691003 scopus 로고
    • Semikinetic modeling of the outflow of ionospheric plasma through the topside collisional to collisionless transition region
    • G.R. WILSON, Semikinetic modeling of the outflow of ionospheric plasma through the topside collisional to collisionless transition region, J. Geophys. Res., 97 (1992), pp. 10551.
    • (1992) J. Geophys. Res. , vol.97 , pp. 10551
    • Wilson, G.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.