Within mathematics regarding differential equations, L-stability is a special case of A-stability, a property of RungeâÂÂKutta 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 RungeâÂÂKutta 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.