Yes, I understood what you explained.
Well, you asked a good question. The answer reflects my limitations in using Maple. Initially, the problem has a PDE system. The material domain varies over time, that is, it is an open physical system (the physical phenomenon is similar to that found in fluid mechanics). I could not resolve this PDE system with the maple, certainly because of my limitations in using the program. Well, to solve this difficulty I approached the problem in an incremental way, decoupling the PDE system from the temporal variable. The result is an ODE system that is calculated with each step of time. That's the reason for all the loops you mentioned.
I am very grateful for your help. Thank you.