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  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 
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Numerical differential equations