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MathGroup Archive 2005

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Re: intermittent crash on numeric solution of elliptic integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62718] Re: [mg62653] intermittent crash on numeric solution of elliptic integral
  • From: Renan <renan.birck at gmail.com>
  • Date: Fri, 2 Dec 2005 05:53:22 -0500 (EST)
  • References: <200511300507.AAA00132@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 11/30/05, Chris Chiasson <chris.chiasson at gmail.com> wrote:
> MathGroup,
>
> The code below shuts down my kernel at seemingly different points in
> the plotting process every time I run it. What does it do for you?

For me (Mathematica 5.0, Linux) it gives me this:

renan@nightfall:~$ math
Mathematica 5.0 for Linux
Copyright 1988-2003 Wolfram Research, Inc.
 -- Motif graphics initialized --


In[1]:= f[x_,m_]=Sqrt[(1+0.176*Sin[m]^2*Sin[x]^2)*(1+1.01769*Sin[m]^2*Sin[x]^2)/(1-
           Sin[m]^2*Sin[x]^2)]
g[W_,m_]=W*46381*10^(-6)*Sqrt[1/(-0.0012245+Sin[m]^2)]
h[m_?NumericQ]:=NIntegrate[f[x,m],{x,ArcSin[0.002/Sin[m]],Pi/2}]
Plot[m[1]/.FindRoot[h[m[1]]\[Equal]g[1,m[1]],{m[1],guess}],{guess,0,1}]
                              2       2                     2       2
             (1 + 0.176 Sin[m]  Sin[x] ) (1 + 1.01769 Sin[m]  Sin[x] )
Out[1]= Sqrt[---------------------------------------------------------]
                                          2       2
                                1 - Sin[m]  Sin[x]

In[2]:=
                              1
        46381 W Sqrt[--------------------]
                                        2
                     -0.0012245 + Sin[m]
Out[2]= ----------------------------------
                     1000000

In[3]:=
In[4]:=

                                  1.000000000000000
Divide::infy: Infinite expression ----------------- encountered.
                                          0

FindRoot::jsing:
                                                                    -8
   Encountered a singular Jacobian at the point {m[1]} = {4.16667 10  }
    . Try perturbing the initial point(s).

                                  1.000000000000000
Divide::infy: Infinite expression ----------------- encountered.
                                          0

FindRoot::jsing:
                                                                    -8
   Encountered a singular Jacobian at the point {m[1]} = {4.16667 10  }
    . Try perturbing the initial point(s).

General::ovfl: Overflow occurred in computation.

General::ovfl: Overflow occurred in computation.

General::ovfl: Overflow occurred in computation.

General::stop: Further output of General::ovfl
     will be suppressed during this calculation.

FindRoot::nlnum:
   The function value {Underflow[] +
                               266
      NIntegrate[f[x, <<6>>2 10    + <<1>>], <<1>>]} is not a list of numbers
                                                266             266
     with dimensions {1} at {m[1]} = {-1.2252 10    + 1.33843 10    I}.

FindRoot::nlnum:
   The function value {Underflow[] +
                               266
      NIntegrate[f[x, <<7>>5 10    + <<1>>], <<1>>]} is not a list of numbers
                                                 266            266
     with dimensions {1} at {m[1]} = {-1.25415 10    + 2.1084 10    I}.

FindRoot::nlnum:
   The function value {Underflow[] +
                               266
      NIntegrate[f[x, <<7>>5 10    + <<1>>], <<1>>]} is not a list of numbers
                                                 266            266
     with dimensions {1} at {m[1]} = {-1.24295 10    + 1.5737 10    I}.

General::stop: Further output of FindRoot::nlnum
     will be suppressed during this calculation.

                                  1.000000000000000
Divide::infy: Infinite expression ----------------- encountered.
                                          0

General::stop: Further output of Divide::infy
     will be suppressed during this calculation.

FindRoot::jsing:
   Encountered a singular Jacobian at the point {m[1]} = {0.0325085}
    . Try perturbing the initial point(s).

General::stop: Further output of FindRoot::jsing
     will be suppressed during this calculation.

FindRoot::lstol:
   The line search decreased the step size to within tolerance specified by
     AccuracyGoal and PrecisionGoal but was unable to find a sufficient
     decrease in the merit function.  You may need more than MachinePrecision
     digits of working precision to meet these tolerances.

FindRoot::lstol:
   The line search decreased the step size to within tolerance specified by
     AccuracyGoal and PrecisionGoal but was unable to find a sufficient
     decrease in the merit function.  You may need more than MachinePrecision
     digits of working precision to meet these tolerances.

FindRoot::lstol:
   The line search decreased the step size to within tolerance specified by
     AccuracyGoal and PrecisionGoal but was unable to find a sufficient
     decrease in the merit function.  You may need more than MachinePrecision
     digits of working precision to meet these tolerances.

General::stop: Further output of FindRoot::lstol
     will be suppressed during this calculation.

Plot::plnr: m[1] /. FindRoot[h[m[1]] == g[1, m[1]], {m[1], guess}]
     is not a machine-size real number at guess = 0.671108.

Plot::plnr: m[1] /. FindRoot[h[m[1]] == g[1, m[1]], {m[1], guess}]
     is not a machine-size real number at guess = 0.648969.

Plot::plnr: m[1] /. FindRoot[h[m[1]] == g[1, m[1]], {m[1], guess}]
     is not a machine-size real number at guess = 0.637992.

General::stop: Further output of Plot::plnr
     will be suppressed during this calculation.

but doesn't seem to quit the kernel, instead it produces a seeming
strange (to me, but I don't have a deep knowledge of differential
equations) graph that can be seen here:

http://img528.imageshack.us/img528/7104/graphofmathgroup3sa.jpg

What do you think?


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