2N-storage Runge-Kutta methods: Order conditions, general properties and some analytic solutions

Low-storage Runge-Kutta schemes of Williamson's type, so-called 2N-storage schemes, are examined. Explicit 2N-storage constraints are derived for the first time and used to establish new relations between the entries of the Butcher tableau. An error in the Williamson's formula for converting coefficients between the standard and 2N-storage formats in the special case is pointed out and corrected. The new relations are used to derive a closed-form solution for four- and five-stage 2N-storage methods with the third order of global accuracy. Several new four- and five-stage schemes with rational coefficients are presented and numerically examined for illustration.