A Q/D-space reformulation of Butcher simplifying assumptions yields sufficient order conditions and a recursive linear-system construction for explicit Runge-Kutta methods of even order p with s(p)=(p²-2p+8)/4 stages.
Numerical methods for ordinary differential equations
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Low Stage High Order Explicit Runge--Kutta Methods via Q- and D-Conditions: General Theory and Efficient Recursive Construction
A Q/D-space reformulation of Butcher simplifying assumptions yields sufficient order conditions and a recursive linear-system construction for explicit Runge-Kutta methods of even order p with s(p)=(p²-2p+8)/4 stages.