FTCS scheme

The FTCS scheme, short for forward time centered space, is a finite difference method used in numerical analysis to solve the heat equation and similar parabolic partial differential equations. It is first order in time and explicit in time, and it is conditionally stable when applied to the heat equation. When it is used for advection equations, or more generally hyperbolic partial differential equations, it is unstable unless artificial viscosity is included. The abbreviation FTCS was first used by Patrick Roache. It is commonly the simplest scheme introduced when explaining how time stepping of a differential equation on a grid can succeed or fail depending on the type of equation being solved.