I want to solve a differential equation lots of times for different parameters. It is more complicated than this, but for the sake of clarity let\'s say the ODE is y\'
Passing an internal procedure is allowed by Fortran 2008. It is not limited to module. You just have to make sure, that the containing procedure is still running. It is not possible to save the pointer and make a so called 'closure' known from LISP and many modern languages. In languages like Fortran or C the enclosing environment for future calls is not saved and pointers to internal functions become invalid.
The advantage of internal procedure over module procedure is that you can share the data without sharing it in the whole module.
It works well will reasonably old versions of GCC (gfortran), Intel Fortran and Cray Fortran (personally tested) and possibly others. I remember not being able to compile by PGI and Oracle Fortran. As shown by Daniel, it can be checked at http://fortranwiki.org/fortran/show/Fortran+2008+status (search Internal procedure as an actual argument). The most recent version of this table is periodically published in ACM SIGPLAN Fortran Forum.
There is some interesting info in this article http://software.intel.com/en-us/blogs/2009/09/02/doctor-fortran-in-think-thank-thunk/