Diffusion as repeated local averaging.
At each interior grid point, the FTCS update looks at the second spatial difference and adjusts the current value accordingly. Sharp local variation gets smoothed as time advances.
Partial differential equations · CMNA Laboratory
Watch a temperature profile forget its sharp edges.
Define the initial temperature in R, then play the forward-time central-space scheme through time.
Bring your own initial condition
Define u₀(x) in R.
Then play the temperature profile through time and watch a space-time heatmap accumulate underneath it.
Runtime
Preparing R…RDefine
u0(x) on 0 ≤ x ≤ 1| time step | min u | mean u | max u |
|---|
Book§7.3.1 · The Heat Equation · p. 219Book details
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