@acer  

Well, in this example (ODE.mw) I used the optimize = true option and this worked very well...

However, the compile option did not work... I saw a discussion on the topic (https://www.mapleprimes.com/questions/205037-Compiletrue-In-Dsolvenumeric) and I confess that I was a bit confused ...

Anyway, I thank you for your clarification.

@Carl Love Perfect! Thank you!

@tomleslie 

The answer is simple: I am a beginner.
Thanks for your help.
I hope your next answers are more friendly.

@Preben Alsholm 

I have a final problem. It consists of a function defined as the integral of a function that is the result of a numerical solution of a PDE.

I need to calculate values for this function (obviously) and also plot it.

Sorry for the 2D entry. Thank you!

Test.mw

@tomleslie I copied the command lines from your file and pasted it into a new tab. Because it does not work?

Test.mw

@mahmood1800 no, because in my problem g (x, t) is a numerical function. It results from a numerical solution of a PDE.

@Preben Alsholm 

Yes, I understand what you have explained and I believe that is the key point.

The procedure I adopted to solve this problem is to discretize the temporal domain and incrementally solve the system at each step of time, taking the function H (t) = cte at each step of time. To do this, I transform the PDE system into an ODE system.

Well, thank you again for your precious help.

@Ramakrishnan 

Well, I'll try to explain.

Removing the function H(t), the PDE system can be transformed into an ODE system (it is possible to remove the dependence of the time differential dt), which has an easy resolution. Finally, the function H (t) is obtained.

Yes, this IBCs is the problem.

Thank you for trying to help me.

@Preben Alsholm 

Sorry for the 2D input. I will change my way of working.

Very interesting the way you work and the way you solved the problem.

You have helped me a lot in the last few days and for that I am grateful. Thank you.

@tomleslie 

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.

@tomleslie 

Can this occur because the functions that define the PDE and its IBCs are numerical in nature?

@Preben Alsholm 

Perfect! Thank you!

@Preben Alsholm 

thanks for your help

@Preben Alsholm 

Test.mw

sorry and thank you