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