I would like to farm out solving systems of ODEs onto GPUs, in a 'trivially parallelisable' setting. For example, doing a sensitivity analysis with 512 different parameter sets, or solving the (independent) ODEs associated with something like nodes of a finite element mesh.Ideally I want to do ODE solving with a smart adaptive timestep solver like CVODE, rather than a fixed timestep like Forward Euler, but running it on an NVIDIA GPU instead of CPU.Has anyone done this? Are there libraries for it? 
Options for solving ODE systems on GPUs?
ode;gpu
You may want to look into Boost's odeint library and Thrust.  They can be combined as discussed here.