L-stability

Short description: Stability property of some Runge–Kutta methods

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 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.

## 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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