Numerical Stability
The property of a numerical algorithm ensuring that errors introduced during computation do not magnify uncontrollably over successive time steps.
Governing formula
Von Neumann Stability Analysis: |G(k, Δt)| ≤ 1
SI unit
Algorithm Stability Property
In depth
In finite difference schemes, numerical instability causes exponential error blow-up. Courant-Friedrichs-Lewy (CFL) condition specifies maximum allowed time step Δt relative to spatial grid spacing Δx.
Examples in the real world
Applying the CFL condition (v Δt / Δx ≤ 1) to prevent numerical explosions in fluid wave simulations.