# Another NDSOLVE::ndsz: … singularity of stiff system suspected

I would be very grateful for any help with my "NDSOLVE::ndsz : At t==0.364197...., step size is effectively zero; singularity of stiff system suspected" error.

Below is my code. I am not free to vary my initial conditions (by much....not more than a few %). I would like to be able to solve this down to t as low as t=0.1 or t=0.05 (I don't need to go to t=0). As of right now, this will only solve for t=0.365 and larger. I tried "ExplicitRungeKutta", "DifferenceOrder"->4*,WorkingPrecision->50, and many of the other options for numerical integration methods, but they don't seem to be any better or worse, and am out of ideas.

q = -0.55;

• Why do you expect that there exists a solution that goes down to $t = 0$? Right now your solution is being driven to $a = 0$ at $t \approx 0.364$, and from the form of your equations it's pretty obvious that you're going to run into problems when that occurs. – Michael Seifert Jul 16 '17 at 20:56
• Ever heard of finite-time singularities? As a plot of the solution suggests, a'[t] tends to infinity for t going to 0.364197... – Henrik Schumacher Jul 16 '17 at 20:56
• Your equation is not stiff, despite the error message. Instead, the calculation fails when a[t] == 0, which happens at t == 0.364197 for the given initial conditions. Therefore, changing NDSolve options has almost no effect. Instead, you need to change the initial conditions. I can look more at the ODE late this evening, if you wish. – bbgodfrey Jul 16 '17 at 22:10
• Sounds like this is the true behavior of the model. I'm not really allowed to change the initial conditions too much.....so it sounds like $a\rightarrow0$ for a finite $t>0$ is a real effect in this model. Thanks for the help. =) – Bob Jul 16 '17 at 22:32