Please note that this statement (IVP numerical methods are more stable compared to BVP methods) is incorrect. Actually, BVP methods are more stable to solve a given BVP problem. It is easy to show many examples to prove the same. For example,
take dy1/dt = y2
dy2/dt = tau^2*y1 + (Pi^2-tau^2)*sin(Pi*t)
IVP: t=0, y1= 0, y2 = Pi
BVP: t= 0, y1 = 0; t = 1, y1 = 0
(Credit: Dr. Biegler at CMU)
This model is very stable with a BVP approach, but not with IVP approach. Shooting method is not useful for largescale or stiff problems. At least multiple shooting is needed.
Add some noise to ics, constants, you will see BVP methods behaving much better.