# 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 as , where is the stability function of the method (the stability function of a Runge–Kutta method is a rational function and thus the limit as is the same as the limit as ). 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.

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