Hello Everyone,

I am trying to solve the spin-up equation for a primordial black hole (PBH) system numerically over a longer integration time. The spin-up equation is given by:

fdot = C_GW*f^{11/3} + C_DF*f^{3/2}

At t=0, f=f_isco. Using time reversal, my equation becomes:

fdot = -C_GW*f^{11/3} - C_DF*f^{3/2}

with the initial condition t=0, f=f_isco.

I am solving this equation using `solve_ivp`

with a step size based on the Nyquist theorem, i.e., step_size = 1/2*f_isco. With this step size, my time vector is t= (0,1e+3,step_size).This setup allows my system to evolve up to 200 Hz.

However, I want to integrate over a longer time span, such as t = (0,1e+8,step_size), to observe the effects of the second term in the spin-up equation, which are usually noticeable below 50 Hz. The problem is that this requires a huge number of steps (around 1e+14), leading to memory errors.

Can anyone suggest a method to solve this equation for a longer time span without running into memory issues?

Thanks!