Re: System of differential-algebraic equations
- To: mathgroup at smc.vnet.net
- Subject: [mg78461] Re: System of differential-algebraic equations
- From: dh <dh at metrohm.ch>
- Date: Mon, 2 Jul 2007 06:53:05 -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[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}]
>