L-stability

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.