Depends on your application. If you are looking for mathematical modeling and analysis, then Python and Matlab are good options. If you want to work with large data (CFD modelling), then C++ and Fortran are preferred languages.

Thank you my dear friend for your answer.

Anant Diwakar is correct. I do agree with him.

Thanks to Anant Diwakar.

The most effective accelerator for learning a new programming language is a supportive group of experienced people. If in your environment the support for all languages is equally good or bad I would select C++ as the only language that was born out of a simulation project. Here you should go for the modern versions C++11 and higher since these contain lots of simplifications compared to the older stuff especially classical C.

The suggestion given by Professor Ulrich Mutze deems fit and proper.

Thanks to Ulrich Mutze.

In provocation, I suggest other languages as being simpler to learn. Should it be that your mathematical model is well defined in terms of matrices, then APL would be an ideal language. It is truly not very hard to learn APL, and is far more powerful than are the other languages listed in other replies to this question.

Thanks to Professor William R. Buckley for giving another suggestion which also seems to be useful.

@William,

APL far more powerful than C++? A provocation indeed!

R LANGUAGE

Based on the experience of writing numerical codes in 4 languages ( Python, Matlab, C++ and Fortran), I would like to state that choosing a language should be based on the application. The same problem can be solved in any language, it's just that it will require more effort in one than in others.

To give an example, I have written spectral codes in Matlab and Python since many required functions/packages are available in them (like Fourier transform, Inverse FFT etc.). Nowadays, people are preferring Python and R for writing codes for machine learning and statistical applications.

However, for writing big codes (CFD), C++ or Fortran are better as they are much powerful in terms of speed and data structures. I have written CFD (FEM and FVM) solvers in Fortran and C++ and they were much faster and efficient as compared to similar effort in Python/Matlab. All the big CFD packages like OpenFOAM, SU2 and Fluent are written in C++/ Fortran.

@William

Not sure about APL as I haven't used it. In its wiki page, it's mentioned that the last stable release was in 2001. That's pretty long back. Not sure that this will be more powerful than C++ as capabilities in these languages (C++, Python etc.) are updated frequently.

I agree with the opinion of Anant Diwakar.

Thanks to Anant Diwakar.

The opinion of Anant Diwakar is very interesting.

Really, it is important to define the main criteria sought, depending on the field of application.

C ++ or Fortran are adequate when speed of execution is paramount.

If this is not the case, some object-oriented programming languages such as Java are also beneficial, as there are many interesting modeling environments like Eclipse EMF that can be used. It will just have a good habit of object oriented philosophy.

They bring model editors, a code skeleton generator to complete, ...

Thanks to Gerard Nzebop for his answer.

Thanks to all of you friends for your useful answers and based on experience advices, I wish you good fortune in the researches to come!

Thanks to Joseph Mousavi for his acknowledgement.

Matlab - Maple

I would recommend ether python or matlab from an engineering and physical science perspective. However, as has been suggested by others already, the choice of an appropriate language will depend on the support structures around you since most problems can be solved in any language

I appreciate the description given by Francis collins Muga.

Thanks to him.

There are many languages, you can use them, as IDEL,Python and Matlab. But from my opinion the Matlab is the best because, the most of its subroutines are available in the wep, you can call them easily.