What is "l-stability"

L-stability is a special case of A-stability, a property of Runge–Kutta methods for solving ordinary differential equations. A method is L-stable if it is A-stable and ϕ(z) → 0 as z → ∞, where ϕ is the stability function of the method (the stability function of a Runge–Kutta method is a rational function and thus the limit as z →  + ∞ is the same as the limit as z →  − ∞). L-stable methods are in general very good at integrating stiff equations.