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Volumn 27, Issue 6, 2011, Pages 1561-1583

Finite difference methods and their physical constraints for the fractional klein-kramers equation

Author keywords

convergence; finite difference method; fractional Klein Kramers equation; stability

Indexed keywords

CONVERGENCE; EXTERNAL FORCE FIELD; FINITE DIFFERENCE; FRACTIONAL KLEIN-KRAMERS EQUATION; NUMERICAL EXAMPLE; NUMERICAL SCHEME; PHASE SPACES; PHYSICAL CONSTRAINTS; RATE OF CONVERGENCE; STABILITY CONDITION; SUBDIFFUSION; THEORETICAL RESULT;

EID: 80052924392     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20596     Document Type: Article
Times cited : (29)

References (27)
  • 2
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • R. Metzler, and, J. Klafter, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Phys Rep 339 (2000), 1-77.
    • (2000) Phys Rep , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 3
    • 4043151477 scopus 로고    scopus 로고
    • The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics
    • R. Metzler, and, J. Klafter, The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics, J Phys A 37 (2004), 161-208.
    • (2004) J Phys A , vol.37 , pp. 161-208
    • Metzler, R.1    Klafter, J.2
  • 4
    • 0033750050 scopus 로고    scopus 로고
    • From a generalized Chapman-Kolmogorov equation to the fractional Klein-Kramers equation
    • R. Metzler, and, J. Klafter, From a generalized Chapman-Kolmogorov equation to the fractional Klein-Kramers equation, J Phys Chem B 104 (2000), 3851-3857.
    • (2000) J Phys Chem B , vol.104 , pp. 3851-3857
    • Metzler, R.1    Klafter, J.2
  • 5
    • 0034205195 scopus 로고    scopus 로고
    • Subdiffusive transport close to thermal equilibrium: From the Langevin equation to fractional diffusion
    • R. Metzler, and, J. Klafter, Subdiffusive transport close to thermal equilibrium: from the Langevin equation to fractional diffusion, Phys Rev E 61 (2000), 6308-6311.
    • (2000) Phys Rev e , vol.61 , pp. 6308-6311
    • Metzler, R.1    Klafter, J.2
  • 6
    • 0036791358 scopus 로고    scopus 로고
    • Combined Hermite spectral-finite difference method for the Fokker-Planck equation
    • J. C. M. Fok, B. Y. Guo, and, T. Tang, Combined Hermite spectral-finite difference method for the Fokker-Planck equation, Math Comp 71 (2001), 1497-1528.
    • (2001) Math Comp , vol.71 , pp. 1497-1528
    • Fok, J.C.M.1    Guo, B.Y.2    Tang, T.3
  • 7
    • 49749096796 scopus 로고    scopus 로고
    • Composite generalized Laguerre-Legendre pseudospectral method for Fokker-Planck equation in an infinite channel
    • T. J. Wang, and, B. Y. Guo, Composite generalized Laguerre-Legendre pseudospectral method for Fokker-Planck equation in an infinite channel, Appl Numer Math 58 (2008), 1448-1466.
    • (2008) Appl Numer Math , vol.58 , pp. 1448-1466
    • Wang, T.J.1    Guo, B.Y.2
  • 8
    • 51749116733 scopus 로고    scopus 로고
    • Finite difference approximations for the fractional Fokker-Planck equation
    • S. Chen, F. Liu, P. Zhuang, and, V. Anh, Finite difference approximations for the fractional Fokker-Planck equation, Appl Math Model 33 (2009), 256-273.
    • (2009) Appl Math Model , vol.33 , pp. 256-273
    • Chen, S.1    Liu, F.2    Zhuang, P.3    Anh, V.4
  • 9
    • 36149001762 scopus 로고    scopus 로고
    • Numerical algorithm for the time fractional Fokker-Planck equation
    • W. H. Deng, Numerical algorithm for the time fractional Fokker-Planck equation, J Comput Phys 227 (2007), 1510-1522.
    • (2007) J Comput Phys , vol.227 , pp. 1510-1522
    • Deng, W.H.1
  • 10
    • 2142755490 scopus 로고    scopus 로고
    • Numerical solution of fractional advection-dispersion equation
    • DOI 10.1061/(ASCE)0733-9429(2004)130:5(422)
    • Z. Q. Deng, V. P. Singh, F. Asce, and, L. Bengtsson, Numerical solution of fractional advection-dispersion equations, J Hydraul Eng 130 (2004), 422-431. (Pubitemid 38554545)
    • (2004) Journal of Hydraulic Engineering , vol.130 , Issue.5 , pp. 422-431
    • Deng, Z.-Q.1    Singh, V.P.2    Bengtsson, L.3
  • 11
    • 17144427014 scopus 로고    scopus 로고
    • The accuracy and stability of an implicit solution method for the fractional diffusion equation
    • DOI 10.1016/j.jcp.2004.11.025, PII S0021999104004887
    • T. A. M. Langlands, and, B. I. Henry, The accuracy and stability of an implicit solution method for the fractional diffusion equation, J Comput Phys 205 (2005), 719-736. (Pubitemid 40518394)
    • (2005) Journal of Computational Physics , vol.205 , Issue.2 , pp. 719-736
    • Langlands, T.A.M.1    Henry, B.I.2
  • 12
    • 4444368867 scopus 로고    scopus 로고
    • Finite difference approximations for fractional advection-dispersion flow equations
    • DOI 10.1016/j.cam.2004.01.033, PII S0377042704000986
    • M. M. Meerschaert, and, C. Tadjeran, Finite difference approximations for fractional advection-dispersion flow equations, J Comput Appl Math 172 (2004), 65-77. (Pubitemid 39204390)
    • (2004) Journal of Computational and Applied Mathematics , vol.172 , Issue.1 , pp. 65-77
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 13
    • 64049113904 scopus 로고    scopus 로고
    • Finite difference approximations for a fractional advection diffusion problem
    • E. Sousa, Finite difference approximations for a fractional advection diffusion problem, J Comput Phys 228 (2009), 4038-4054.
    • (2009) J Comput Phys , vol.228 , pp. 4038-4054
    • Sousa, E.1
  • 14
    • 25444472344 scopus 로고    scopus 로고
    • An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations
    • DOI 10.1137/030602666
    • S. B. Yuste, and, L. Acedo, An explicit finite difference method and a new Von Neumann-type stability analysis for fractional diffusion equations, SIAM J Numer Anal 42 (2005), 1862-1874. (Pubitemid 41634613)
    • (2005) SIAM Journal on Numerical Analysis , vol.42 , Issue.5 , pp. 1862-1874
    • Yuste, S.B.1    Acedo, L.2
  • 15
    • 55549107511 scopus 로고    scopus 로고
    • New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation
    • P. Zhuang, F. Liu, V. Anh, and, I. Turner, New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation, SIAM J Numer Anal 46 (2008), 1079-1095.
    • (2008) SIAM J Numer Anal , vol.46 , pp. 1079-1095
    • Zhuang, P.1    Liu, F.2    Anh, V.3    Turner, I.4
  • 16
    • 59349113701 scopus 로고    scopus 로고
    • Finite element method for the space and time fractional Fokker-Planck equation
    • W. H. Deng, Finite element method for the space and time fractional Fokker-Planck equation, SIAM J Numer Anal 47 (2008), 204-226.
    • (2008) SIAM J Numer Anal , vol.47 , pp. 204-226
    • Deng, W.H.1
  • 17
    • 42649109055 scopus 로고    scopus 로고
    • Numerical approximation of a time dependent, nonlinear, space-fractional diffusion equation
    • DOI 10.1137/050642757
    • V. J. Ervin, N. Heuer, and, J. P. Roop, Numerical approximation of a time dependent, nonlinear, space-fractional diffusion equation, SIAM J Numer Anal 45 (2007), 572-591. (Pubitemid 351599168)
    • (2007) SIAM Journal on Numerical Analysis , vol.45 , Issue.2 , pp. 572-591
    • Ervin, V.J.1    Heuer, N.2    Roop, J.P.3
  • 18
    • 14644446063 scopus 로고    scopus 로고
    • Least squares finite-element solution of a fractional order two-point boundary value problem
    • DOI 10.1016/j.camwa.2004.10.003, PII S0898122104003438
    • G. J. Fix, and, J. P. Roop, Least squares finite element solution of a fractional order two-point boundary value problem, Comput Math Appl 48 (2004), 1017-1033. (Pubitemid 40319749)
    • (2004) Computers and Mathematics with Applications , vol.48 , Issue.7-8 , pp. 1017-1033
    • Fix, G.J.1    Roof, J.P.2
  • 19
    • 33845751607 scopus 로고    scopus 로고
    • A second-order accurate numerical method for a fractional wave equation
    • DOI 10.1007/s00211-006-0045-y
    • W. Melean, and, K. Mustapha, A second-order accurate numerical method for a fractional wave equation, Numer Math 105 (2007), 481-510. (Pubitemid 44974242)
    • (2007) Numerische Mathematik , vol.105 , Issue.3 , pp. 481-510
    • McLean, W.1    Mustapha, K.2
  • 20
    • 34547548712 scopus 로고    scopus 로고
    • Finite difference/spectral approximations for time-fractional diffusion equation
    • Y. Lin, and, C. Xu, Finite difference/spectral approximations for time-fractional diffusion equation, J Comput Phys 225 (2007), 1533-1552.
    • (2007) J Comput Phys , vol.225 , pp. 1533-1552
    • Lin, Y.1    Xu, C.2
  • 21
    • 77958536189 scopus 로고    scopus 로고
    • A space-time spectral method for the time fractional diffusion equation
    • X. J. Li, and, C. Xu, A space-time spectral method for the time fractional diffusion equation, SIAM J Numer Anal 47 (2009), 2018-2131.
    • (2009) SIAM J Numer Anal , vol.47 , pp. 2018-2131
    • Li, X.J.1    Xu, C.2
  • 22
    • 37649007901 scopus 로고    scopus 로고
    • Numerical approach to the fractional Klein-Kramers equation
    • M. Magdziarz, and, A. Weron, Numerical approach to the fractional Klein-Kramers equation, Phys Rev E 76 (2007), 066708.
    • (2007) Phys Rev e , vol.76 , pp. 066708
    • Magdziarz, M.1    Weron, A.2
  • 25
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • Ch. Lubich, Discretized fractional calculus, SIAM J Math Anal 17 (1986), 704-719.
    • (1986) SIAM J Math Anal , vol.17 , pp. 704-719
    • Lubich, Ch.1
  • 27
    • 59349102367 scopus 로고    scopus 로고
    • Ergodic properties of fractional Brownian-Langevin motion
    • W. H. Deng, and, E. Barkai, Ergodic properties of fractional Brownian-Langevin motion, Phys Rev E 79 (2009), 011112.
    • (2009) Phys Rev e , vol.79 , pp. 011112
    • Deng, W.H.1    Barkai, E.2


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