Professor Eisenberg:
Thanks a lot for taking the time to scrutinize the code and relay in writing your observations. I really appreciate your effort and feel thankful for it. Per your notes, I proceeded as follows:
[01] Clearly understood your point on evaluating cells one-by-one instead the entire notebook.
[02] I was not aware of the precedence's need during function declaration. This area is clear now.
[03] Currently I am investigating how to avoid using a "For" loop with other constructs (i.e. Table).
[04] Per your note, RK4 and f have been changed to return a result.
[05] Variable i removed from f since it was not being used.
[06] With your observations regarding precedence of functions and their return of values now can state code as: k1 = h f[x, yn], etc...
[07] Not using symbol, *, for multiplication helps in de-cluttering the code.
[08] In RK4 the inputs (x, y, m, h) are declared globally to accommodate variants of initial value problems.
[09] Coefficients declaration (i.e. k1,...) changed and this makes their intent more clear.
[10] With all your observations, the code have been changed and the need for TWICE evaluation is abolished!!!
Currently I will use your observations on a package to solve BVP. Please be sure that as I found setbacks, I will seek the advise of experts like you on this forum.
Thanks!!!
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