Isomeric trees and the order of Runge–Kutta methods

The conditions for a Runge–Kutta method to be of order p with p≥5 scalar non-autonomous problem are proper subset the vector problem. Nevertheless, methods that were derived historically only problems happened same problems. We relate factorisations trees into “atomic stumps” and enumerate those up p=20. Using special search procedure over unsatisfied conditions, new “ambiguous orders” five six constructed. These used verify validity results.