I am solving a system of non linear differential equations. The time needed to solve them is quite long and I would like to shorten it. Is it possible to send the NDSolve command to be solved by the GPU using CUDALink?
No, that's not possible. If you could show your code there might be other ways to speed it up.
There is no library that I am aware of that does the trick. So there is no easy solution on it. Anyway, there is a publication about CUDA and parabolic PDEs. Do a search on "CUDA Jahn Uni Bayreuth" in the internet. There is a pdf (diploma Dissertation). May be that helps to find a solution for your problem; adding the problem to learn German ;).