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[1]/.FindRoot[h[m[1]]\[Equal]g[1,m[1]],{m[1],guess}],{guess,0,1}] Version Number: 5.2.0.0 Platform: Windows Regards, -- http://chrischiasson.com/contact/chris_chiasson