       Re: System of differential-algebraic equations

• To: mathgroup at smc.vnet.net
• Subject: [mg78310] Re: System of differential-algebraic equations
• From: dh <dh at metrohm.ch>
• Date: Thu, 28 Jun 2007 04:21:34 -0400 (EDT)
• References: <f5tbnq\$24q\$1@smc.vnet.net>

```
Hi Jose,

your system is not consistent. E.g. the initial conditions do not

fullfill the first equation.

hope this helps, Daniel

José Luis Gómez 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[m][t]*x[t]^2 +

>

>      m[t]*x[t]*Derivative[x][t] + (1/3)*DerivaFrom - Wed Jun 27 14:38:12 2007
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