PDE Zoo: Wave, Heat, Laplace, Schrodinger and Burgers

Pick an equation and watch the same finite-difference grid behave completely differently. The wave equation conserves energy and oscillates; the heat equation only ever smooths and fades; the Laplace/Poisson equation skips time entirely and jumps to the steady shape; the Schrodinger equation keeps its total probability fixed while the wavepacket spreads; and Burgers, the one-dimensional cousin of Navier-Stokes, sharpens a smooth wave into a shock that viscosity then rounds off. For the cases with a known exact solution the analytic curve is drawn behind the numeric one and the gap between them is plotted as the error, so you can see how good the numerical method is. A Crank-Nicolson scheme advances each equation, and where an exact solution exists the analytic curve is drawn behind the numeric one so the discretisation error is visible.