Picard-Green , Mann-Green and Ishikawa-Green methods are new and best.

All numerical methods are Iterative methods I think

I suggest you to follow : https://homepage.divms.uiowa.edu/~atkinson/papers/NAODE_Book.pdf

https://people.maths.ox.ac.uk/suli/nsodes.pdf

https://www.cs.bgu.ac.il/~leonid/ode_bio_files/Ionascu_LectNotes.pdf

https://au.mathworks.com/help/matlab/math/choose-an-ode-solver.html

http://faculty.olin.edu/bstorey/Notes/DiffEq.pdf

Good Luck

You can try this paper:

https://www.sciencedirect.com/science/article/pii/S1018364718303112

and the references therein. Also, these are nice papers:

Article New Numerical Methods for Solving Differential Equations

Article Simplified variational iteration method for solving ordinary...

Waleed Hajo

Not true!

Finite Difference Methods are numerical methods BUT NOT iterative!

Picard iteration = Successive iteration.

Suitable to treat nonlinear DEs.

Newton"s Method!

Thesis Homotopy type methods for nonlinear differential equations

Picard-Green , Mann-Green and Ishikawa-Green methods are new and best.