Heat Equation on a Rod (Finite Difference)
Parameters
Diffusivity (α):
0.20
Initial condition:
Gaussian bump
Step function
Single sine
Multi-sine
Random
Left BC:
0
Right BC:
0
Run
Reset
PDE:
∂u/∂t = α ∂²u/∂x²
Scheme:
Explicit finite difference. Stability requires α·Δt/Δx² ≤ ½.
The rod visualizes temperature as color (blue→red). The plot shows the profile over time. Fourier modes decay exponentially at rate α·k².