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Diffusion Equation Explorer
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Diffusivity
ฮฝ (diffusivity)
0.010
Initial Condition
Shape
Gaussian
Square Pulse
Sine Mode
Double Gaussian
Triangle
Near-Delta
Amplitude A
1.0
Width ฯ
0.06
Numerical Setup
Grid N
200
Stability r
0.45
Scheme
FTCS (Forward-Time)
Crank-Nicolson
BTCS (Implicit)
Boundary Conditions
Type
Periodic
Dirichlet (u=0)
Neumann (flux=0)
Display
Exact (Fourier)
Numerical
Initial profile
Fill under curve
Animation
Speed
1.0
ร
Loop at T
5.0
Live Stats
Lยฒ error:
โ
ฯ(t) spread:
โ
ฯโโ(1+2ฮฝt/ฯโยฒ):
โ
max|u|:
โ
โซu dx:
โ
๐ก๏ธ Evolution
๐ต Fourier Modes
๐ Spreading
๐ฌ Scheme Compare
โถ Play
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t = 0.000
r = 0.45
u(x, t) โ Temperature / Concentration
|u_exact โ u_numerical|
Fourier Spectrum |รป_k| โ modes decay as e^(โฮฝkยฒt)
ฯ(t) โ Diffusive Spreading ฯโโ(1 + 2ฮฝt/ฯโยฒ)
FTCS vs Crank-Nicolson vs BTCS vs Exact
t = 0.000
r = โ
Lยฒ = โ
mass = โ
FTCS
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