1D Heat Equation

∂u/∂t = α ∂²u/∂x² — explicit (FTCS) vs. implicit (Crank-Nicolson) solvers

Initial Condition

Solver

r = α·Δt/Δx² =
Stability:
Time: t = 0.000
FTCS (explicit): stable only when r ≤ 0.5
Crank-Nicolson: unconditionally stable, 2nd-order in both x and t

Watch what happens as r > 0.5 — oscillations appear in the explicit solver. CN stays smooth.

Colormap: blue (cold) → red (hot)
The waterfall shows time evolution.