Thus, we obtain the difference equation
![](Images/image023.png)
Denoting we get
![](Images/image027.png)
The general solution of this equation is
![](Images/image029.png)
where is an arbitrary constant and
![](11_3_clip_image002.gif)
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
![](Images/image043.png)
and we can write
![](Images/image045.png) |