I am working on deriving the explicit and implicit Runge Kutta methods. And here is my temporatory work Runge Kutta methods.
In general, the Runge Kutta order $p$ method, i.e., $ \displaystyle O\left( {{{h}^{{p+1}}}} \right)$ need some numbers of step $s$. In wiki introduction, one have bounded $\displaystyle \min s$ for the explicit Runge Kutta order $p$ method. I wonder if there is a above bound for $s$, i.e., $\displaystyle \max s$ for the explicit Runge Kutta order $p$ method and the implicit ones?