Assume the exact result is \( \tilde{x} \) and that we are using an RKM method. Suppose we run two calculations, one with \( h \) (called \( x_1 \)) and one with \( h/2 \) (called \( x_2 \)). Then $$ \tilde{x}=x_1+Ch^{M+1}+O(h^{M+2}), $$ and $$ \tilde{x}=x_2+2C(h/2)^{M+1}+O(h^{M+2}), $$ with \( C \) a constant. Note that we calculate two halves in the last equation. We get then $$ |x_1-x_2| = Ch^{M+1}(1-\frac{1}{2^M}). $$ yielding $$ C=\frac{|x_1-x_2|}{(1-2^{-M})h^{M+1}}. $$ We rewrite $$ \tilde{x}=x_2+\epsilon+O((h)^{M+2}), $$ with $$ \epsilon = \frac{|x_1-x_2|}{2^M-1}. $$