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Keywords
(2)
Numerical Solution
Fractional Advection Dispersion Equation
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Numerical Solution of the Fractional AdvectionDispersion Equation
Numerical Solution of the Fractional AdvectionDispersion Equation,F. Liu,V. Ahn,I. Turner
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Numerical Solution of the Fractional AdvectionDispersion Equation
(
Citations: 3
)
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F. Liu
,
V. Ahn
,
I. Turner
Published in 2002.
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Citation Context
(3)
...Reactiondifiusion 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 onedimensional reactiondifiusion 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 Baeumer
,
et al.
Numerical solutions for fractional reactiondiffusion 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. Meerschaert
,
et al.
Finite difference approximations for twosided spacefractional 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. Meerschaert
,
et al.
Finite difference approximations for fractional advectiondispersion &...
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Citations
(3)
Numerical solutions for fractional reactiondiffusion equations
(
Citations: 8
)
Boris Baeumer
,
Mihály Kovács
,
Mark M. Meerschaert
Journal:
Computers & Mathematics With Applications  COMPUT MATH APPL
, vol. 55, no. 10, pp. 22122226, 2008
Finite difference approximations for twosided spacefractional partial differential equations
(
Citations: 53
)
Mark M. Meerschaert
,
Charles Tadjeran
Journal:
Applied Numerical Mathematics  APPL NUMER MATH
, vol. 56, no. 1, pp. 8090, 2006
Finite difference approximations for fractional advectiondispersion &ow equations
(
Citations: 36
)
Mark M. Meerschaert
,
Charles Tadjeran