A Q/D-space framework supplies sufficient order conditions for explicit Runge-Kutta methods and supports a recursive construction of even-order methods with stage count (p²-2p+8)/4.
Some Explicit Runge–Kutta Methods of High Order
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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 framework supplies sufficient order conditions for explicit Runge-Kutta methods and supports a recursive construction of even-order methods with stage count (p²-2p+8)/4.