       Re: NDSolve and DAEs

• To: mathgroup at smc.vnet.net
• Subject: [mg124613] Re: NDSolve and DAEs
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Thu, 26 Jan 2012 03:30:58 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201201251204.HAA05991@smc.vnet.net>

```eqns = {
x1'[t] == x2[t],
x2'[t] == -x3[t] - x2[t],
x3'[t] == x2[t] x4[t],
x4'[t] == -x3[t] x2[t]};

ics = {x1 == 0.5, x2 == 0,
x3 == Sin[0.5], x4 == Cos[0.5]};

sol = NDSolve[Join[eqns, ics], {x1, x2, x3, x4}, {t, 0, 16}][];

x3 x3 + x4 x4 == 1 /. sol

True

Plot[Evaluate[{
Tooltip[x1[t], "x1"],
Tooltip[x2[t], "x2"],
Tooltip[x3[t], "x3"],
Tooltip[x4[t], "x4"]} /. sol],
{t, 0, 16}]

Bob Hanlon

2012/1/25 J. Jes=FAs Rico Melgoza <jerico at umich.mx>:
> Hi everybody!
>
> I have the following DAE system:
>
> eqns = {x1'[t] == x2[t], x2'[t] == -x3[t] - x2[t],
>
x3'[t] == x2[t] x4[t],
>
x4'[t] == -x3[t] x2[t]}
> with initial conditions
>
> ics = {x1 == 0.5, x2 == 0, x3 == Sin[0.5],
>
x4 == Cos[0.5]}
> that must satisfy the following constraint
>
> x3x3+x4x4=1
> The interval of time is {t,0,16}.
>
> I do not know how to do it with NDSolve.
> Can this be done? in some part of the documentation there is an example
> where the enqs are linear but the same procedure applied to my problem
> (nonlinear) wouldn't work.
>
> I will appreciate any help.