What is L-stability?

Within mathematics regarding differential equations, 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 → 0 {\displaystyle \phi \to 0} as z → ∞ {\displaystyle z\to \infty } , where ϕ {\displaystyle \phi } is the stability function of the method. L-stable methods are in general very good at integrating stiff equations.