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System of differential-algebraic equations
*To*: mathgroup at smc.vnet.net
*Subject*: [mg78271] System of differential-algebraic equations
*From*: José Luis Gómez <jose.luis.gomez at itesm.mx>
*Date*: Wed, 27 Jun 2007 05:29:43 -0400 (EDT)
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}]
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