Best ODE solver when there is a parameter discontinuity

Hello,

I have a system of differential equations where one of the parameters changes value abruptly at one point in time. Which ODE solver is the most accurate and most efficient to use in such a situation? I'm trying to use ode45, but when I use a low tolerance, I'm not getting an accurate answer. When I try to tighten, the tolerance, it is taking an extremely long time to run (it's been running over an hour and still hasn't finished).

Thank you, Kevin