See how heat diffuses along a rod — Fourier series decomposition solving the PDE in real time
Temperature Profile (click/drag to set)
Fourier Coefficients aₙ
u_t = α u_xx on [0,L] with u(0,t)=u(L,t)=0. Solution: u(x,t) = Σ aₙ sin(nπx/L) exp(−α(nπ/L)²t). Higher modes decay faster — low frequencies persist longest. Draw your own initial profile by clicking and dragging on the canvas.