Is there any free utility/software to generates and numerically solve the field equation for modified gravity $f(R)$ I'm looking for a free software (preferred to run under Windows) that can generate the gravity field equations for a given $f(R)$ model in modified gravity. 
I used Maxima to calculate a few terms, but i wounder if there is any Maxima package that specific deal with $f(R)$? 
More important, i'm looking for a free util/software that numerically solve the gravity field equation for a specific $f(R)$ model. My FLRW equations are very steep. I tried running Runge Kutta with Maxima and other steep ODE solver methods with Scilab, but im not getting a good results. FLRW are highly depends on the initial condition.
I do wounder which software a professional researchers in the universities are using to calculate those equations?
 A: The best option is xAct in mathematica. It has really good functionality, and I've just used it to do some research into EGBS gravity which it handled really well. I'm also pretty sure there are some $f(R)$ examples on the xAct github and the google group is pretty good and is really responsive. However, this does mean you have to get mathematica which is quite expensive. However, if you are planning on doing further work in the area you might want to get it. If you are at college/uni then your institution might have a licence you can use if you ask.
The other option, something I've never personally used but have had recommended to me by colleagues, is Cadabra. It can handle GR-like calculations and it is designed specifically for field theory calculations and I believe it is free. It works a little like mathematica and xAct but I've been told it is a little more intuitive since it has been designed solely for field theory calculations. It works with tensors, and is programmable in Python.
