Question

When I numerically solving a ode with the following code, warnings named “evfrf” prompted.

I am wondering how to force variables of differential equations to be Real numbers

NDSolve[{y''[t] + .1 y'[t] + Sin[y[t]] == 0, y'[0] == 1, 
y[0] == 0}, y, {t, 0, 20}, 
Method -> {"EventLocator", "Event" -> y[t], 
"EventCondition" -> y'[t] > 0, 
"EventAction" :> Print[t, ", ", y[t], ", ", y'[t]]}]

warning message:

NDSolve::evfrf: 
The event function did not evaluate to a real number somewhere 
between t =  1.5798366385128957` and t = 1.6426647495929725`,
preventing FindRoot from finding the root accurately. >>  

Thanks 🙂

Answer 1

I don’t think this is an issue of the answer genuinely being a complex number at those points.
The following does not give an error.

sol = NDSolve[{y''[t] + .1 y'[t] + Sin[y[t]] == 0, y'[0] == 1, 
 y[0] == 0}, y, {t, 0, 20}]

Plot[y[t] /. sol, {t, 0, 20}]

The issue is the attempt to find the zero in y'[t] and limitations in the implied root-finding process. I tried increasing the WorkingPrecision and the MaxSteps but it didn’t remove the error.

sol = NDSolve[{y''[t] + .10`64 y'[t] + Sin[y[t]] == 0, y'[0] == 1, 
y[0] == 0}, y, {t, 0, 20}, 
  Method -> {"EventLocator", "Event" -> y[t], 
 "EventCondition" -> y'[t] >= 0, 
 "EventAction" :> Print[t, ", ", y[t], ", ", y'[t]]},  
   MaxSteps -> 10^9, MaxStepSize -> 0.0001, WorkingPrecision -> 32]

Unless you really care about the eighth or subsequent decimal place, I would suggest not worrying about this error.

Those more expert than me in numerical analysis might disagree, but I work in a field where we usually don’t have any faith in the accuracy of any data past the first decimal place of a percentage change (third decimal place of a level).