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[MUG] HOWTO solve system where solution is piecewise?
| [MUG] HOWTO solve system where solution is piecewise? |
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Author:
Posted: Thu, 28 Nov 2002 15:29:14 +0100
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>> From: "stef.pillaert"
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| [MUG] HOWTO solve system where solution is piecewise? |
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Author: Stef Pillaert
Posted: Tue, 3 Dec 2002 09:24:22 +0100
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>> From: "Stef Pillaert" "stef.pillaert"
Hello,
suppose I'm looking for the function that is the solution of the following
system of eq.:
for all values of x, dy(x)/dx=1 OR dy/dx is not defined, but the function
has a jump from some value y1 to y2=y1+x.
The BC's are y(0)=0 and y(4)=5
A solution to this problem is: piecewise(x<1,x,x>=1, x+1).
Is there a way to make MAPLE find this solution?
Thanks,
Stef.
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| [MUG] Re: HOWTO solve system where solution is piecewise? |
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Author: Maple User Group
Posted: Fri, 6 Dec 2002 18:04:53 -0500 (
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>> From: Maple User Group "maple_gr"
-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-
From: "Ivan Huerta" "ihuerta"
To: "maple-list"
Subject: HOWTO solve system where solution is piecewise?
Date: Wed, 4 Dec 2002 18:00:08 -0400
Hi:
The following may be of some help....
> sol:=dsolve( {diff(y(t),t) = 1+ A*Dirac(t-a), y(0)=0}, y(t));
sol := y(t) = A Heaviside(t - a) + t - A Heaviside(-a)
> Ysol:= unapply(subs(sol,y(t)),t);
Ysol := t -> A Heaviside(t - a) + t - A Heaviside(-a)
> A:=solve( Ysol(4)=5,A);
1
A := - ---------------------------------
-Heaviside(4 - a) + Heaviside(-a)
> Ysol(t);
Heaviside(t - a) Heaviside(-a)
- --------------------------------- + t
+ ---------------------------------
-Heaviside(4 - a) + Heaviside(-a) -Heaviside(4 - a) +
Heaviside(-a)
Any value of a, with 0 < a < 4 works. The solution you provide is obtained
by setting
> a:=1;
a := 1
> Ysol(t);
Heaviside(t - 1) + t
Regards,
Prof. Ivan Huerta
Facultad de Matematicas
Pontificia Universidad Catolica de Chile
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Date: Thu, 05 Dec 2002 18:31:11 +0000
Subject: HOWTO solve system where solution is piecewise?
To: "maple-list"
From: John Trapp "j.j.trapp"
The question is not properly posed.
A solution to this problem is: piecewise(x<a,x,x>=a, x+1) where a is in
]0,4[
Or can one have a solution of the form: piecewise(x<a,x,a<=x<b, x+0.5,
b<=x, x+1)
John
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