Heat Equation on a Rod (Finite Difference)

Parameters

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.