I've been trying to solve differential equations of the form
$$\dot{\rho}=\omega L\rho$$
where $\omega=\omega(t)$ is scalar 1/f (or pink) noise and $L$ and $\rho$ are matrices.
I wanted to know if there were any recommended numerical schemes to solve it. I have looked into the Taylor-RODE scheme (described here: https://pdfs.semanticscholar.org/f357/b5b871bc704659bf18507135eea9f57a5fa4.pdf) but it doesn't seem very efficient (involves various integrals and such). I was hoping to find a nice efficient SDE-resembling scheme to solve it. I saw some papers on forming nonlinear and/or coupled SDEs for just 1/f noise.
https://arxiv.org/pdf/1603.03013.pdf
http://web.vu.lt/tfai/j.ruseckas/files/presentations/Turkey-2012.pdf
https://arxiv.org/pdf/1003.1155.pdf
I wanted to know if anyone had implemented solutions to SDEs like these and if anyone has a good idea on how to extend it properly and efficently to these matrix equations.
If there are any other nice schemes or ideas you have, please let me know as well!
Thanks!