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2012 | 10 | 1 | 101-115

Tytuł artykułu

A finite difference approach for the initial-boundary value problem of the fractional Klein-Kramers equation in phase space

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Języki publikacji

EN

Abstrakty

EN
Considering the features of the fractional Klein-Kramers equation (FKKE) in phase space, only the unilateral boundary condition in position direction is needed, which is different from the bilateral boundary conditions in [Cartling B., Kinetics of activated processes from nonstationary solutions of the Fokker-Planck equation for a bistable potential, J. Chem. Phys., 1987, 87(5), 2638–2648] and [Deng W., Li C., Finite difference methods and their physical constrains for the fractional Klein-Kramers equation, Numer. Methods Partial Differential Equations, 2011, 27(6), 1561–1583]. In the paper, a finite difference scheme is constructed, where temporal fractional derivatives are approximated using L1 discretization. The advantages of the scheme are: for every temporal level it can be dealt with from one side to the other one in position direction, and for any fixed position only a tri-diagonal system of linear algebraic equations needs to be solved. The computational amount reduces compared with the ADI scheme in [Cartling B., Kinetics of activated processes from nonstationary solutions of the Fokker-Planck equation for a bistable potential, J. Chem. Phys., 1987, 87(5), 2638–2648] and the five-point scheme in [Deng W., Li C., Finite difference methods and their physical constrains for the fractional Klein-Kramers equation, Numer. Methods Partial Differential Equations, 2011, 27(6), 1561–1583]. The stability and convergence are proved and two examples are included to show the accuracy and effectiveness of the method.

Wydawca

Czasopismo

Rocznik

Tom

10

Numer

1

Strony

101-115

Opis fizyczny

Daty

wydano
2012-02-01
online
2011-12-09

Twórcy

  • Southeast University
  • Southeast University

Bibliografia

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  • [3] Cartling B., Kinetics of activated processes from nonstationary solutions of the Fokker-Planck equation for a bistable potential, J. Chem. Phys., 1987, 87(5), 2638–2648 http://dx.doi.org/10.1063/1.453102
  • [4] Chen S., Liu F., Zhuang P., Anh V., Finite difference approximations for the fractional Fokker-Planck equation, Appl. Math. Model., 2009, 33(1), 256–273 http://dx.doi.org/10.1016/j.apm.2007.11.005
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  • [7] Deng W., Li C., Finite difference methods and their physical constrains for the fractional Klein-Kramers equation, Numer. Methods Partial Differential Equations, 2011, 27(6), 1561–1583 http://dx.doi.org/10.1002/num.20596
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