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 ( z ) → 0 {\displaystyle \phi (z)\to 0} as z → ∞ {\displaystyle z\to \infty } , where ϕ {\displaystyle \phi } 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 → + ∞ {\displaystyle z\to +\infty } is the same as the limit as z → − ∞ {\displaystyle z\to -\infty } ). L-stable methods are in general very good at integrating stiff equations.
References Hairer, Ernst; Wanner, Gerhard (1996), Solving ordinary differential equations II: Stiff and differential-algebraic problems (second ed.), Berlin: Springer-Verlag, section IV.3, ISBN 978-3-540-60452-5.
