A very nice article on how to use boost::odeint and SIMD:

Boosting ODE simulations with Boost.odeint and Boost.SIMD

by Mario Mulansky

From the article:

Ordinary Differential Equations appear in numerous applications and finding their solution is a fundamental problem in science and engineering. Often one has to rely on numerical methods to approximate such solutions as in the presence of nonlinearities, no analytic solution can be found. Being such a frequent problem...