<P> In numerical analysis, the FTCS (Forward - Time Central - Space) method is a finite difference method used for numerically solving the heat equation and similar parabolic partial differential equations . It is a first - order method in time, explicit in time, and is conditionally stable when applied to the heat equation . When used as a method for advection equations, or more generally hyperbolic partial differential equation, it is unstable unless artificial viscosity is included . The abbreviation FTCS was first used by Patrick Roache . </P> <P> The FTCS method is based on central difference in space and the forward Euler method in time, giving first - order convergence in time and second - order convergence in space . For example, in one dimension, if the partial differential equation is </P> <Dl> <Dd> ∂ u ∂ t = F (u, x, t, ∂ 2 u ∂ x 2) (\ displaystyle (\ frac (\ partial u) (\ partial t)) = F \ left (u, x, t, (\ frac (\ partial ^ (2) u) (\ partial x ^ (2))) \ right)) </Dd> </Dl>

Prove that the forward in time centered spacing differencing scheme is unconditionally unstable