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Math Help - stiff ode solving

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    1

    Unhappy 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
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  2. #2
    Super Member
    Joined
    Aug 2008
    Posts
    903
    Quote Originally Posted by hadidehghanzade View Post
    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?
    Attached Thumbnails Attached Thumbnails stiff ode solving-bending-reed.jpg  
    Last edited by shawsend; September 25th 2009 at 06:50 AM.
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