During trying to solve a differential equation using numerical methods like RK methods (Runge Kutta) , one has to factor in important stuff like stability of the the system , whether the equations are stiff or not. For that , appropriate step size has to be considered.
However, as I have read that equations becomes stiff due transient spikes due to which step-size need to be smaller. However, I am aware of schemes like Adaptive RK Method where we can move along x , adjusting the step size as per the local error per step. Why can't this step control in Adaptive RK Method be used to account in stability itself ?
Quoting the book , "Stability requirement will still necessitate using very small steps throughout the entire solution".