# Math Help - stiff ode solving

1. ## stiff ode solving

Dear friends,

My problem is a kind of stiff ordinary differential equation of 11 first order equations (state space equations). I have tried to solve it by ode15s and ode23s but there are some situations that the integrator is not successful and fails to integrate, the message which is displayed is shown below please let me know how to solve the problem.

Warning: Failure at t=2.694000e+002.
Unable to meet integration tolerances
without reducing the step size below the
smallest value allowed (9.094947e-013) at
time t.
> In ode15s at 753

please let me know how to solve the problem.
Take for example, the equation:

$y'=\frac{3x^2}{3y^2-4},\quad y(1)=0$

If I try to numerically integrate that I get:

Code:
In[105]:=
Clear[x, y]
NDSolve[{Derivative[1][y][x] ==
(3*x^2)/(3*y[x]^2 - 4), y[1] == 0},
y, {x, 1, 2}]

During evaluation of In[105]:=
NDSolve::ndsz:At x == 1.597809453897525,
step size is effectively zero;
singularity or stiff system suspected. >>

Out[106]=
{{y -> InterpolatingFunction[]}}`
The (full) solution is below. Why is the integrator giving me that message?