FTCS scheme

Summary

The FTCS scheme, for "forward time, centred space", is the simplest finite difference method for the heat equation. It replaces the time derivative by a forward difference and the second space derivative by a centred difference. So each new value is computed explicitly from three old ones. It is first-order accurate in time and second-order accurate in space. It is stable only under the condition $\alpha \Delta t / \Delta x^2 \le 1/2$, which forces very small time steps on fine grids. See the definition.