At the end of the second paragraph, it says:
"For this reason, the Dormand–Prince method is more suitable when the higher-order solution is used to continue the integration, a practice known as local interpolation (Hairer, Nørsett & Wanner 1993)."
But my 2008 copy of the same book (corrected 3rd printing) calls it "local EXTRAPOLATION"!
I'm changing it, correct me if you have better information than my own (and if you do, explain why,please!)
Regards, Jose Brox