       Re: System of differential-algebraic equations

• To: mathgroup at smc.vnet.net
• Subject: [mg78299] Re: System of differential-algebraic equations
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 28 Jun 2007 04:15:56 -0400 (EDT)
• Organization: Uni Leipzig
• References: <f5tbnq\$24q\$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de

```Hi,

if you don't have initial conditions that satisfy the
algebraic constrains, than there is *no* solution and
you are done -- no Mathematica, no NDSolve[]

You can try FindInstance[] to find valid initial
conditions but the input is than random ...

You can try to set boundary conditions instead of
initial conditions but this will change the character
of the problem.

Regards
Jens

Jos=E9 Luis G=F3mez 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 thi=
s
> 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 va=
lues.
> We fool around a bit in the documentation, play a little bit with
> AccuracyGoal, and PrecisionGoal, and with different methods specified b=
y
> Method, but we were not able to obtain an answer.
>
>
>
> Does anyone have a suggestion for us? Can we avoid the use of initial v=
alues
> 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)*Derivative[q][t]*
>
>       x[t]^3 + q[t]*x[t]^2*Derivative[x][t] -
>
>      (25.2/10^15)*q[t]*x[t] == 0,
>
>    0.444*Derivative[x][t]*0.5*r[t]*(y[t] - x[t])^2 +
>
>      (1/3)*Derivative[u][t]*(y[t] - x[t])^3 +
>
>      (Derivative[y][t] - Derivative[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[v][t]*(y[t] - 140/10^16)^2 +
>
>      v[t]*(y[t] - 140/10^6)*Derivative[y][t] +
>
>      (1/3)*Derivative[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., q == 2.342*^8, r == =
3.7843*^7,
>
>    u == -1.385*^13, v == 0., w == 1.9856*^7,
>
>    x == 1.7/10^6, y == 4.42/10^6}, {m, q, r, u, v, w, x, =
y},
>
>   {t, 0, 3600}]
>

```

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