The number of conditions for a Runge-Kutta method to have effective order p Original Research Article

We count the number of conditions that a one-step numerical integrator has to satisfy to achieve a given effective order of accuracy p. Effective order refers to the order of the numerical method after the numerical solution has been enhanced by suitable pre- and post-processors. The methods considered include not only Runge-Kutta methods, but also all methods that can be represented by B-series, such as multiderivative generalizations of Runge-Kutta methods.