Problem with DSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg131595] Problem with DSolve
• From: "Hagwood, Charles R" <charles.hagwood at nist.gov>
• Date: Tue, 10 Sep 2013 03:33:26 -0400 (EDT)
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I am having a problem using NDSolve to solve the following differential equation

gamma[s_,a_]:=s+16*a*s^2*(s-1)^2

beta2[s_]:={Cos[2*Pi*s],Sin[2*Pi*s]}
q2[s_]:=beta2'[s]/Sqrt[Norm[beta2'[s]]]

beta1[s_,a_]:={Cos[2*Pi*gamma[s,a]],Sin[2*Pi*gamma[s,a]]}
dbeta1[x_,a_]:=D[beta1[s,a],s]/.s->x
q1[x_,a_]:=dbeta1[x,a]/Sqrt[Norm[dbeta1[x,a]]]

h1[x_]:=q2[x].q2'[x]
h2[x_]:=q2[x].q2[x]

NDSolve[{6*y'[x]^2*q1[x,.3].q2'[y[x]] +6*y'[x]^(5/2)*h1[y[x]]+y''[x]*q1[x,.3].q2[y[x]]-y''[x]*y'[x]^(1/2)*h2[y[x]]==0,y[0]==0,y[1]==1},y,{x,0,1}]

I get the error :

NDSolve::nlnum: "The function value {1.49012*10^-8,0.159096\ (-1.33227*10^-15\ (2.50786\ (-1.51364*10^-10+Times[<<2>>])-0.00161827\ (-15.7496+Times[<<2>>]))-1.6263*10^-19\ (2.50663\ (-<<24>>+Times[<<2>>])-<<1>>))} is not a list of numbers with dimensions {2} at {x,NDSolve`Shooting`ShootingDump`x\$1395[x]} = {0.00010264848819015064`,{1.5295816688262022`*^-12,1.4901161193847656`*^-8}"

Also, I noticed that when I try to evaluate the objective  function  Mathematica does not evaluate it.  For example, let

y[x_]:=x+16*(.3)*x^2*(x-1)^2

(6*y'[x]^2*(q1[x,.3].q2'[y[x]]) +6*y'[x]^(5/2)*h1[y[x]]+y''[x]*(q1[x,.3].q2[y[x]])-y''[x]*y'[x]^(1/2)*h2[y[x]])/.x->.2
I get

8.88178*10^-16+22.1553 (-1.53612 (-14.127+0.00701735 (-196.722 (Abs^\[Prime])[-0.442082]-196.722 (Abs^\[Prime])[0.896975]))-3.11675 (6.96262 +0.014238(-196.722 (Abs^\[Prime])[-0.442082]-196.722 (Abs^\[Prime])[0.896975])))+30.712 (-1.10814 (-14.127+0.00701735 (-196.722 (Abs^\[Prime])[-0.442082]-196.722 (Abs^\[Prime])[0.896975]))-2.24838 (6.96262 +0.014238 (-196.722 (Abs^\[Prime])[-0.442082]-196.722 (Abs^\[Prime])[0.896975])))

Thanks

Charles Hagwood

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