Module 3: Higher order Single Step Methods
  Lecture 11: Absolute Stability for Runge-Kutta Methods
 

 

Thus, we obtain the difference equation

Denoting we get

The general solution of this equation is

where is an arbitrary constant and

We can then define the three-stage Runge-Kutta method to be absolutely stable on the interval is , as given above, satisfies , whenever .

If the Runge-Kutta method under discussion is consistent, then

and we can write