You won't be able to use or parallelize the ddriv3
call without some effort. Your usage of the phrase "parallel loop" suggests to me you may be thinking of using OpenACC directives with Fortran, as opposed to CUDA Fortran, but the general answer isn't any different in either case.
The ddriv3
call, being part of a Fortran library (which is presumably compiled for x86 usage) cannot be directly used in either CUDA Fortran (i.e. using CUDA GPU kernels within Fortran) or in OpenACC Fortran, for essentially the same reason: The library code is x86 code and cannot be used on the GPU.
Since presumably you may have access to the source implementation of ddriv3
, you might be able to extract the source code, and work on creating a CUDA version of it (or a version that OpenACC won't choke on), but if it uses many other library routines, it may mean that you have to create CUDA (or direct Fortran source, for OpenACC) versions of each of those library calls as well. If you have no experience with CUDA, this might not be what you want to do (I don't know.) If you go down this path, it would certainly imply learning more about CUDA, or at least converting the library calls to direct Fortran source (for an OpenACC version).
For the above reasons, it might make sense to investigate whether a GPU library replacement (or something similar) might exist for the ddriv3
call (but you specifically excluded that option in your question.) There are certainly GPU libraries that can assist in solving ODE's.