       Re: bvdae error when using NDSolve for initial value

• To: mathgroup at smc.vnet.net
• Subject: [mg102098] Re: [mg102063] bvdae error when using NDSolve for initial value
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Wed, 29 Jul 2009 05:11:12 -0400 (EDT)
• References: <200907280605.CAA14835@smc.vnet.net>

```The error message is complaining, I think, about the equation

w[u]==w1[u]+w2[u]

Also, the equation

T'[u] == 0

makes T a constant.

Hence, solving for T and w with NDSolve makes no sense.

In addition, you can't specify "timer" both at 0 AND at 1, because then
you have too many equations. If you eliminate some other equation, the two
values for "timer" are probably inconsistent.

Here's a code that works, at least, though it may not do everything you
want:

Clear[w1, w2, timer, w]
w[u_] = w1[u] + w2[u];
T = 1;
NDSolve[{w1'[u] == T w1[u]/w[u] (w1[u]/w[u])^(1 - \[Epsilon]),
w2'[u] == T w2[u]/w[u] (w2[u]/w[u])^(1 - \[Epsilon]),
timer'[u] == T (p1 w1[u] + p2 w2[u]), timer == 0, w1 == 3/2,
w2 == 1} /. {p1 -> 1/100, p2 -> 1/100, \[Epsilon] -> 1/2}, {w1,
w2, timer}, {u, 0, 1}]

Bobby

On Tue, 28 Jul 2009 01:05:14 -0500, Damon <damonwischik at gmail.com> wrote:

> I am trying to solve an initial value problem. I am getting the error
> message "bvdae: Differential-algebraic equations must be given as
> initial value problems". I don't know what the error means or how to
> fix my equations. I would be grateful for any help.
>
> I started with the following differential equations. I want to find
> the time T when timer[T]==8.3 (or some other arbitrary value), and I
> want to evaluate w1[T] and w2[T] at that time.
>
> res = NDSolve[{
> w1'[u]==w1[u] 1/w[u] (w1[u]/w[u])^(1-\[Epsilon]),
> w2'[u]==w2[u] 1/w[u] (w2[u]/w[u])^(1-\[Epsilon]),
> w[u]==w1[u]+w2[u],
> timer'[u]==(p1 w1[u]+p2 w2[u]),
> timer==0,
> w1==1.5,
> w2==1
> } /. {p1->.01,p2->.01,\[Epsilon]->.5},
> {w1,w2,w,timer},{u,0,11}
> ]
>
> I transformed this into an initial value problem in standard form as
> follows.
>
> Clear[w1,w2,timer];
> res = NDSolve[{
> w1'[u]==T[u] w1[u] 1/w[u] (w1[u]/w[u])^(1-\[Epsilon]),
> w2'[u]==T[u] w2[u] 1/w[u] (w2[u]/w[u])^(1-\[Epsilon]),
> w[u]==w1[u]+w2[u],
> T'[u]==0,
> timer'[u]==T[u] (p1 w1[u]+p2 w2[u]),
> timer==0,
> w1==1.5,
> w2==1,
> timer==8.3
> } /. {p1->.01,p2->.01,\[Epsilon]->.5},
> {w1,w2,w,T,timer},{u,0,1}
> ]
>
> This gives me the error I quoted at the top of this post. I would be
> grateful for hints about what I should do to solve my problem.
>
> Damon.
>

--
DrMajorBob at bigfoot.com

```

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