Stiffness

A property of an ODE that forces explicit methods to take tiny steps for stability.

Definition

A problem is stiff when very different time scales coexist: fast components that have already decayed still limit the step of explicit methods, even though the visible solution is smooth. Accuracy would allow a large step; stability forbids it.

How it is used

The typical sign: RK4 blows up except with absurdly small steps while implicit Euler proceeds calmly. Switch to implicit or A-stable methods.