Stages vs. Order in numerical analysis for ODE

69 Views Asked by At

I'm reading this interesting book by Butcher.

I do not understand what are the definitions of stages and orders of numerical methods.

I think that these 2 terms are somewhat overloaded.

Which page for their definitions should I consult in the book to grasp them both?

EDIT:

I think that at least order has 2 different meaning: one of them being exact for polynomials of order at most $p$ and the other that the error converges as fast as $\cal{O}(h^{p+1})$.

EDIT Stages and orders I have located stages and orders in the book but I'm still unaware what do the notions mean.

enter image description here

enter image description here

ORDER

enter image description here