You introduce some new notations here (k, Y) that should be added to your Table of Symbols.
This could be my unfamiliarity with RK methods, but doesn't second order come before fourth order? Can you swap the table order to reflect this please?
Most of the side notes you have in brackets () could be incorporated into the body text with some rewriting, and I think it would help with readability.
Some more smaller points to deal with: