Professor Eisenberg:
Thanks again for taking the time to review my post. Attached a practice notebook with your guides. I am learning a lot from your insightful comments. Below are some notes from your post. Porting code from explicit to implicit iteration is beneficial and now I have a better understanding of it. Great leanings from you.
Thanks
Definition Of Function f:
[01] In f, argument x is used for non-homogeneous ODE or BVP.
[02] Defining f per your guidelines help clarify doubts on my side and makes its intent clear. Thanks!
Definition Of Function RK4:
[03] I realize the behavior of a variable, like k1, etc..., once an assignment occurs, hence impracticality for constant arrays. Thanks!
[04] It is clear your points on yn1. Thanks!
[05] It is clear also the comment on parameter m. Thanks!
[06] Great point on avoiding approximate use and how to maneuver with N. Thanks!
[07] Use of (**) is a habit that I should stop. Space helps. Thanks!
The Iteration: From Explicit Loop To Implicit Iteration
[08] The form you state RK4step is very clever and clear. Now I understand the type of changes. Thanks!
[09] The guides for stating NestList with RK4step is very clear. Looks like a controlled recursion. VERY HELPFUL. Thanks!
[10] Stating newRK4 gives new understanding on how to program. Thanks!
[11] Cleaning and customizing the output of lis is very helpful as well as insightful. I was expecting major difficulties. Thanks!
[12] The function nicerRK4 and RK4 are very compact and clear. Great learning from them. Thanks!
Printing A Nice Table Of Results:
[13] TableForm with RK4 does a straight job of showing results. Very useful. Thanks!
Further Refinements:
[14] Using f as argument to RK4step and RK4 is something that I am exploring. What would be the benefit(?)
[15] Input Checking is a good safeguard. Thanks for noting it.
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