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Re: Problem with discontinuity in NDSolve[]
*To*: mathgroup at smc.vnet.net
*Subject*: [mg4429] Re: [mg4301] Problem with discontinuity in NDSolve[]
*From*: Andrei Constantinescu <constant at xanthe.polytechnique.fr>
*Date*: Mon, 22 Jul 1996 01:19:41 -0400
*Sender*: owner-wri-mathgroup at wolfram.com
Dear Axel,
there is a fundamental math problem with your system.
If you compute [e:
NDSolve[{y'[t] == 10 - y[t] * If[t-15 <= 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 at athena.polytechnique.fr
LMS Ecole Polytechnique tel: (33)-1-69.33.33.30
91128 PALAISEAU cedex - FRANCE fax: (33)-1-69.33.30.26
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