Runge–Kutta methods
Runge–Kutta methods for the numerical solution of formula_62 replace the differential equation by a discrete equation formula_76, where the rational function formula_59 is characteristic of the method, and formula_8 is the time step size. If formula_79 whenever formula_80, then a stable differential equation, having formula_73, will always result in a stable (contractive) numerical method, as formula_82. Runge-Kutta methods having this property are called A-stable.