B-series and Applications. The order of Runge–Kutta and General Linear Methods

Given an initial value problem y'(x) = f(y(x)), y(x_0) = y_0, and a unit time distance h, many questions can be asked, such as
I. What is the solution at x = x_0 +h?
II. What is the approximate solution at x = x_0 +h, computed by a Runge–Kutta method?
These can be typically written as series (a “B-series”). One of our aims will be to become familiar with the quantities appearing in this series.
Link to join: (Note the new link and new time) https://eu.bbcollab.com/guest/0074554a69294e48aa8198be3579464f