RV: System of differential-algebraic equations

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• Subject: [mg78372] RV: [mg78271] System of differential-algebraic equations
• From: José Luis Gómez <jose.luis.gomez at itesm.mx>
• Date: Fri, 29 Jun 2007 05:49:15 -0400 (EDT)

```You are very kind to use your time for answering our question, even it was a
bad question (sorry for that!) I will check your suggestions. Thank you!

Jose

-----Mensaje original-----
De: DrMajorBob [mailto:drmajorbob at bigfoot.com]
Enviado el: Mi=E9rcoles, 27 de Junio de 2007 02:25 p.m.
Para: Jos=E9 Luis G=F3mez
Asunto: Re: [mg78271] System of differential-algebraic equations

Attached is a partial solution for the initial conditions.

I took only the first solution at one point, and it may not be a
MEANINGFUL solution. You should look at that further with the underlying
problem in mind.

After evaluating subFunction[m]...

m[t] and Subscript[m,t] are interchangeable, they both evaluate to m[t],
and they both display in the subscripted form. I often find that
convenient.

You can take out the first cell without affecting the rest of the
notebook, except for the way the functions are displayed.

Bobby

On Wed, 27 Jun 2007 04:29:43 -0500, Jos=E9 Luis G=F3mez
<jose.luis.gomez at itesm.mx> wrote:

> Dear Mathematica Group.
>
>
> A colleague has asked me help to solve a system of 8 algebraic and
> differential equations. The system is included below, at the end of this
> e-mil, in InputForm.
>
> Mathematica 6.0 NDSolve command replies with this message:
>
>
> NDSolve::icfail: Unable to find initial conditions which satisfy the
> residual function within specified tolerances.  Try giving initial
> conditions for both values and derivatives of the functions.
>
>
> Now, my colleague does not want to give initial conditions for the
> derivatives, because he does not have actual information about those
> values.
> We fool around a bit in the documentation, play a little bit with
> AccuracyGoal, and PrecisionGoal, and with different methods specified by
> Method, but we were not able to obtain an answer.
>
>
> Does anyone have a suggestion for us? Can we avoid the use of initial
> values
> for the derivatives?
>
>
> The system is included below. Thanks in advance for any advice.
>
>
> Jose Luis Gomez-Munoz
>
>
>
>
> NDSolve[{m[t]*x[t] + q[t]*x[t]^2 == 2.75,
>
>    (12.6/10^15)*m[t]^2 - (10.2/10^16)*m[t]*r[t] -
>
>      (20.4/10^16)*m[t]*u[t]*y[t] + (20.4/10^16)*m[t]*u[t]*x[t] -
>
>      (92.4084/10^15)*q[t] == 0,
>
>    r[t]*(y[t] - x[t]) + u[t]*(y[t] - x[t])^2 == 0.444,
>
>    (10.2/10^16)*r[t]^2 - (9.82/10^12)*r[t]*v[t] -
>
>      (389.9256/10^16)*u[t] == 0, v[t] + 2*w[t]*(y[t] - 140/10^16) ==
>
>     0, 0.5*Derivative[1][m][t]*x[t]^2 +
>
>      m[t]*x[t]*Derivative[1][x][t] + (1/3)*Derivative[1][q][t]*
>
>       x[t]^3 + q[t]*x[t]^2*Derivative[1][x][t] -
>
>      (25.2/10^15)*q[t]*x[t] == 0,
>
>    0.444*Derivative[1][x][t]*0.5*r[t]*(y[t] - x[t])^2 +
>
>      (1/3)*Derivative[1][u][t]*(y[t] - x[t])^3 +
>
>      (Derivative[1][y][t] - Derivative[1][x][t])*
>
>       (r[t]*(y[t] - x[t]) + u[t]*(y[t] - x[t])^2) -
>
>      (20.4/10^16)*u[t]*(y[t] - x[t]) == 0,
>
>    0.5*Derivative[1][v][t]*(y[t] - 140/10^16)^2 +
>
>      v[t]*(y[t] - 140/10^6)*Derivative[1][y][t] +
>
>      (1/3)*Derivative[1][w][t]*(y[t] - 140/10^6)^3 +
>
>      (19.64/10^12)*w[t]*(140/10^6 - y[t]) + w[t]*(y[t] - 140/10^6)^2*
>
>       y[t] == 0, m[0] == 0., q[0] == 2.342*^8, r[0] == 3.7843*^7,
>
>    u[0] == -1.385*^13, v[0] == 0., w[0] == 1.9856*^7,
>
>    x[0] == 1.7/10^6, y[0] == 4.42/10^6}, {m, q, r, u, v, w, x, y},
>
>   {t, 0, 3600}]
>
>

--
DrMajorBob at bigfoot.com

```

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