       intermittent crash on numeric solution of elliptic integral

• To: mathgroup at smc.vnet.net
• Subject: [mg62653] intermittent crash on numeric solution of elliptic integral
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Wed, 30 Nov 2005 00:07:17 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```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?
BTW, this code is related to someone else's MathGroup post. I was
trying to show that different guesses for the initial condition
actually lead to different initial conditions and to different
solutions for a differential equation ( D[h[m[W]]==g[W,m[W]],W] - you
know, Carl Woll's homotopic extension method ).

The other day, I learned that when Plot::plnr complains about
"something" not being a machine-size real number at blah blah blah
(exact quote :-] ), the "something" is always the held form of the
first Plot slot; thus, the message does not show exactly what
expression isn't numeric... You might notice that phenomena in the
output of the code below, if the kernel makes it that far.

By the way, does anyone know if any of the expressions below are of a
form that could be represented by some combination of the
EllipticIntegral type built-in functions?

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/.FindRoot[h[m]\[Equal]g[1,m],{m,guess}],{guess,0,1}]

Version Number: 5.2.0.0
Platform: Windows

Regards,
--
http://chrischiasson.com/contact/chris_chiasson

```

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