How to derive Runge-Kutta methods?
Using an explicit Runge-Kutta method, how can you determine the order of the method (the order of the truncation error), by looking at the Butcher tableau?
For example, according to wikipedia, the midpoint method is not the optimal RK2 (second order) method. How comes? In wich way may other RK2 methods be more optimal?
Is there some general way to derive a Butcher tableau for a Runge-Kutta method if you know that you want it to be in a certain number of stages? Is there some way to obtain an 'optimal' tableau?