WOLFRAM|DEMONSTRATIONS PROJECT

Numerical Solution of Some Fractional Diffusion Equations

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weight parameter λ
0.5
anomalous diffusion exponent γ
0.5
size of the timestep Δt
1.×
-6
10
number of timesteps
0
normal solution
u(x, 0)
double tent
sin(π x)
4 x(1-x)
δ(x-1/2)
fractional Crank–Nicolson method
The method is stable: the solution will remain finite.
This Demonstration shows numerical solutions
u(x,t)
of the fractional diffusion equation by means of weighted average methods (or
θ
methods). The boundary conditions specify that the solution
u
equals zero at
x=0
and
x=1
. Four different initial conditions can be chosen. When the weight parameter
λ=1-θ
equals 1/2, the numerical method is the fractional Crank–Nicolson method. When the "normal solution" checkbox is checked, the normal diffusion solution is also plotted.