You can find a lot of books explaing the FD method for such problems but you will find general illustrations, the coding in a specific language such as Fortran is not often detailed...

You can find sources written in Matlab in the clawpack software http://www.clawpack.org/

your request is more for a topic of homeworks...

Thank you Filippo, In fact this is the first time for me to use Fortran so I'm looking for some examples to save some time. actually I already used Python for solving these kind of equations in the past with no problems.

Alvioli thank you, it is always good to go back to the numerical recipe

Numerical Heat Transfer by S. Patankar is a great book in this field. It explains the basis for writing good algorithms. However, it would be necessary to write a code in one of the languages such as Fortran.

T. DebRoy

Thank you DebRoy

I would recommend that you read "Computational Techniques for Fluid Dynamics" by C.A.J. Fletcher.

Thank you Mišo Bjelić , I never checked this book before