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Re: [mg4301] Problem with discontinuity in NDSolve[]
Posted:
Jul 17, 1996 1:38 AM


Dear Axel,
there is a fundamental math problem with your system.
If you compute [e:
NDSolve[{y'[t] == 10  y[t] * If[t15 <= 0, 0, 1], y[0] == 0}, y, {t,0,20}]
the solution is simple because the system has two behaviours one for t < 0 and another one for t > 0. So everything is nice.
But if you write:
NDSolve[{y'[t] == 10  y[t] * If[y[t]15 <= 0, 0, 1], y[0] == 0}, y, {t,0,20}]
then the system has also two behavoiurs one for y < 0 and another one for y > 15 .
Unfortunately each time as the system reaches y = 15, its switching to the second exponential behaviour, but then the solutions also decreases so you arrive again at y < 0, and you switch again,
... which gives a neverendind story, and of course the computation never converges !
In order to obtain a behaviour until y reaches 15 and another one after (even if y < 15 again !), you have to introduce an internal parameter, governing the swich: alpha = 0 until y = 15 alpha = 1 if y was already been 15 ... which means another equation to your problem of the sort:
alpha == If[ alpha == 1  y == 15 , 1 , 0 ]
a + andrei
______________________________________________________________________ Andrei Constantinescu constant@athena.polytechnique.fr LMS Ecole Polytechnique tel: (33)169.33.33.30 91128 PALAISEAU cedex  FRANCE fax: (33)169.33.30.26



