Prob with NDSolve in Mathematica

Barnak

How can I show the regular part of the solution of a differential equation, numerically solved with NDSolve, if there's a singularity on the curve ?

I know how to use NDSolve and show its solution, but Mathematica gives a bad curve after some point (singularity jumping). I don't want to show this part, just the regular curve BEFORE the singularity (which is occuring at t = %$&*).

More precisely, the curve function should be strictly positive : a[t] > 0. The NDSolve should stop the resolution if a <= 0. I added the command StoppingTest -> (a[t] < 0.001) or StoppingTest -> (a[t] <= 0) but it doesn't work. I'm still getting wrong curve parts with a[t] < 0.

Any idea ?

kai_sikorski

Why don't you just solve over the interval you're solving over now, but only plot it over the interval where it's positive?

Barnak

Duh ! Because I don't know in advance what are the singularities !

There are two singularities on the curve, and I need to plot the regular part between them. There's no way I can know in advance the exact values of the singularities.

phyzguy

Try using Sow and Reap inside the NDSolve, and only Sow when the answer meets your criterion, as in the attached notebook.

Attached Files

Sow_Reap_Interpolating_Function.nb (27.0 KB, 3 views)

Barnak

Very good trick ! Thanks a lot for that info !

However, I found the right solution to my problem : I just have to define the x values at which the curve y[x] blows away, like this :

Then, I plot the curve between these two values.

kai_sikorski

I don't see how that's different than what I suggested.. but glad it worked for you

Barnak

Actually, it's exactly what you suggested. I just wasn't able to see how to implement it at first.