       Re: Diff. Equations with "Changeable" Parameters

• To: mathgroup at smc.vnet.net
• Subject: [mg51693] Re: Diff. Equations with "Changeable" Parameters
• From: p-valko at tamu.edu (Peter Valko)
• Date: Fri, 29 Oct 2004 03:39:37 -0400 (EDT)
• References: <clpsou\$abt\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```You need an initial condition for x as well.
Then a right hand side function definition is handy:

f[x_, y_] := x + Sin[t] + 1*y; -1 < y && y < 1;
f[x_, y_] := x + Sin[t] + 0*y; y <= -1;
f[x_, y_] := x + Sin[t] + 2*y; 1 <= y;

NDSolve[{x'[t] == y[t], y'[t] == f[x[t], y[t]],
y == 0, x == 0}, {x[t], y[t]}, {t, 0, 2Pi}]

The result will be:
{{x[t] -> InterpolatingFunction[{{0., 6.28319}}, <>][t],
y[t] -> InterpolatingFunction[{{0., 6.28319}}, <>][t]}}

Regards
Peter

"Krunom Ilicevic" <krunom at hotmail.com> wrote in message news:<clpsou\$abt\$1 at smc.vnet.net>...
> I have solved diff. equations in this kind of a way:
>
> NDSolve[{x'[t]=y[t],y=0}, {y'[t]=x+Sin[t]+c*y[t]},{x,y},{t,0,2Pi}]
>
> and parameter c was 1, but how to write this algorithm if c is:
>
> c=0, if y<=-1
>
> c=1, if -1<y<1
>
> c=2, if y>=1
>
> How to include this variable parameter c in my NDSolve method?
>
>
>
> Thanks.

```

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