 Step-doubling error estimation

For an order-$p$ one-step method with leading numerical error $C{h}^{p+1}$, two half steps have leading error $C{h}^{p+1}/2^p$. The displayed difference estimates exact minus the finer approximation. Adding it implements Richardson extrapolation. It requires a common starting value, the smooth local expansion, and accuracy of all algebraic solves; it can fail across a nonsmooth event.