Use the results of Exercise 32 in Section 5.4 to show that the Runge-Kutta method of order four is consistent.
In Exercise 32
The Runge-Kutta method of order four can be written in the form
w0 = α,
wi+1 = wi + h/6 f (ti ,wi) + h/3 f (ti + α1h,wi + δ1hf (ti ,wi))
+ h/3 f (ti + α2h,wi + δ2hf (ti + γ2h,wi + γ3hf (ti ,wi)))
+ h/6 f (ti + α3h,wi + δ3hf (ti + γ4h,wi + γ5hf (ti + γ6h,wi + γ7hf (ti ,wi)))).
Find the values of the constants
α1, α2, α3, δ1, δ2, δ3, γ2, γ3, γ4, γ5, γ6, and γ7