# Understanding NDSolve::ndsz

I'm working on a largeish system of differential equations where I encounter the NDSolve::ndsz step size is effectively zero; singularity or stiff system suspected error.

Since this error arises from the complexity of the system I'm not able to distill a minimum example, but there might still be some useful general information we can share.

In particular I'd like to know:

• What's the difference between stiffness and a singularity? How can I tell whether my sysetm is singular or stiff?

• What quantity is Mathematica calculating to decide if the system is stiff/singular? Can I calculate this quantity myself to see what property of my system is causing problems?

• Have you seen this? reference.wolfram.com/mathematica/tutorial/… – Dr. belisarius Dec 18 '13 at 16:00
• Ad.1) Both stiffness and singularity will limit the step size used by the integration method. Ad. 2) "A convenient way of detecting stiffness is to directly estimate the dominant eigenvalue of the Jacobian of the problem ..." quote from reference given by belisarius. – mmal Dec 19 '13 at 0:07