# 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 ${\displaystyle \phi (z)\to 0}$ as ${\displaystyle z\to \infty }$, where ${\displaystyle \phi }$ is the stability function of the method (the stability function of a Runge–Kutta method is a rational function and thus the limit as ${\displaystyle z\to +\infty }$ is the same as the limit as ${\displaystyle z\to -\infty }$). 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.