ODE solvers - why is Matlab ode45 uncannily stable?

[stevengj]

@TS-CUBED

I was wondering if the speed-up should be that dramatic, since I assume ode45 is implemented in c, so should be fast as well.

Your right-hand-side is implemented in Matlab, and it needs to be called multiple times per step, so that is generally the limiting factor in the speed for Matlab ODEs.