I'm solving a differential equation numerically by

NDSolve[{p'[r] == -function[r,p[r]], p[0] == pcenter}, p,{r, 0, rmax}]

with function>0. At some r, p[r] becomes negative. I want NDSolve to stop as soon as this happens and save the value of r. Any ideas how to do this?

  • 1
    $\begingroup$ WhenEvent is what you want $\endgroup$
    – acl
    Jul 12, 2014 at 12:52
  • $\begingroup$ exactly. thank you! $\endgroup$
    – dan-ros
    Jul 12, 2014 at 12:54
  • $\begingroup$ @acl I posted an answer using what I learned from your comment. Thanks! By the way, I'm involving you in an experiment without your permission (sorry!) $\endgroup$
    – Ian
    Jun 5, 2015 at 21:50
  • $\begingroup$ @Ian excellent, up voted. Happy to serve as a guinea pig. $\endgroup$
    – acl
    Jun 5, 2015 at 22:41
  • $\begingroup$ @lan I read through your experiment. I feel reluctant to formally accept your answer though because I never actually tested the code $\endgroup$
    – dan-ros
    Jun 7, 2015 at 16:10

1 Answer 1


A WhenEvent[event, action] can be included in the list eqn used in NDSolve[eqn,__]. For example:

eqn = {
  p'[r] == -p[r] - 1,
  p[0] == 1,
  WhenEvent[p[r] == 0, rMax = r; "StopIntegration"]
sol = NDSolve[eqn, p, {r, 0, \[Infinity]}];
Plot[p[r] /. sol, {r, 0, rMax}]
  • 4
    $\begingroup$ FYI: The last r is in fact the endpoint of the domain of the solution. The domain may be obtained with p["Domain"] /. sol. (Of course, it can be convenient to save it in a variable rMax as you did, too.) $\endgroup$
    – Michael E2
    Jun 5, 2015 at 22:18

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