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 $\phi(z) \to 0$ as $z \to \infty$ , where $\phi$ is the stability function of the method (the stability function of a Runge–Kutta method is a rational function and thus the limit as $z \to +\infty$ is the same as the limit as $z \to -\infty$ ). L-stable methods are in general very good at integrating stiff equations.

References

{{citation | first1 = Ernst | last1 = Hairer | first2 = Gerhard | last2 = Wanner | year = 1996 | title = Solving ordinary differential equations II: Stiff and differential-algebraic problems | edition = second | publisher = Springer-Verlag | location = Berlin | isbn = 978-3-540-60452-5 | at = section IV.3}}.

Category:Numerical differential equations