We used some python functions explain briefly what they do:

$($a$)$ y$=$odeint $($dydt$.$yO$,$t$)$

$($b$)$ I$=$quad $($f$,$a$,$b$)$

$($c$)$ popt,pcov$=$curvefit $($func$,$xdata,ydata,pO$)$

$($d$)$ w$.$v$=$eightridiagonal$($d$,$e$)$

$($e$)$ r$=$newton $($f$,$df$,$x$0)$