       Problem with discontinuity in NDSolve[]

• To: mathgroup at smc.vnet.net
• Subject: [mg4301] Problem with discontinuity in NDSolve[]
• From: a_kowald at chemie.fu-berlin.de (Axel Kowald)
• Date: Tue, 9 Jul 1996 00:46:47 -0400
• Organization: Kristallographic Institute FU Berlin
• Sender: owner-wri-mathgroup at wolfram.com

```Hi everybody,

I have a problem with NDSolve if my equation contains a discontinuity.
If I try

NDSolve[{y'[t] == 10 - y[t] * If[y[t]-15 <= 0, 0, 1],
y == 0}, y, {t,0,20}]

I always get the error:  Maximum number of steps reached.
The solution should be a linear increase until y = 15 followed by an
exponential decay until a steady state is reached by y = 10

Funny enough if I try

NDSolve[{y'[t] == 10 - y[t] * If[t-15 <= 0, 0, 1],
y == 0}, y, {t,0,20}]

causing the discontinuity to be at t = 15 instead of y = 15 NDSolve has no
problems at all. (But of course this is not what I want.)

ANY SOLUTIONS ???     ANY IDEAS  ???

Many thanks

Axel Kowald

P.S. I'm using Mma 2.2 on a Mac with 7.5.3 and 24 MB RAM

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