A stiff differential equation is an ordinary differential equation for which some numerical methods require an impractically small step size for stability, even where the exact solution varies slowly. Stiffness commonly occurs when the solution contains components with widely separated decay rates. For example, the scalar test equation
 |
is stiff over an interval when 
is large and negative relative to the time scale of
interest.
Explicit methods have bounded stability regions and may therefore be inefficient for stiff systems. Implicit methods, including backward differentiation formulas and implicit Runge-Kutta methods, are designed to have the stronger stability properties needed for such problems.
