Isomeric trees with applications to Runge-Kutta methods
John Butcher @ (University of Auckland)
Classical Runge–Kutta methods, up to the work of Nyström, were derived to achieve a required order for scalar problems, even though they often retained the same asymptotic accuracy for high-dimensional problems. By writing trees in terms of products of what will be referred to as atomic factors, the distinction between scalar and vector conditions is seen to be equivalent to identifying permuted products with the same factors. These interrelated trees are said to be “isomeric".
The number of conditions for order
The first method of order