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Numerical Solution of the Fractional Advection-Dispersion Equation

Numerical Solution of the Fractional Advection-Dispersion Equation,F. Liu,V. Ahn,I. Turner

Numerical Solution of the Fractional Advection-Dispersion Equation   (Citations: 3)
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Published in 2002.
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    • ...Reaction-difiusion equations are useful in many areas of science and engineering [1, 2, 3, 4, 5]. In applications to population biology, the reaction term models growth, and the difiusion term accounts for migration [6, 7]. The classical difiusion term originates from a model in physics [8, 9]. Recent research indicates that the classical difiusion equation is inadequate to model many real situations, where a particle plume spreads faster ...
    • ...Other approaches include variations on the method of lines [30, 31, 32], a flnite element scheme [33, 34, 35], and particle tracking [36]...
    • ...The classical one-dimensional reaction-difiusion equation (1.1) @u(x;t) @t = D @ 2 u(x;t) @x 2 + ~ f(u(x;t)); u(x;0) = u0(x) is used in population biology to model the spread of invasive species [6, 7]. Here u(x;t) is the population density at location x 2R and time t > 0. The flrst term on the right is the difiusion term; it models migration...
    • ...corresponds to a commonly used discrete time model in population biology [6, 7, 37]...
    • ...In this context, the probability density f¿(x) is called a dispersal kernel, since it represents the distance travelled by a randomly selected member of the species during one time step of duration ¿ [7, 71]...

    Boris Baeumeret al. Numerical solutions for fractional reaction-diffusion equations

    • ...A dierent method for solving the fractional partial dierential equation (1.1) is pursued in the recent paper of Liu, Ahn and Turner [6]...

    Mark M. Meerschaertet al. Finite difference approximations for two-sided space-fractional partia...

    • ...A di�erent method for solving the fractional partial di�erential Eq. ( 1) is pursued in the recent paper of Liu et al. [18]...

    Mark M. Meerschaertet al. Finite difference approximations for fractional advection-dispersion &...

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