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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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