Mathematica: Infinite expression error when using NDSolve

[stephanie22]

Dear all,

If someone could help me solve this mathematica NDSolve problem, that would be really nice. Here is a related, simpler problem to the one I am having. Suppose I want to solve the nonlinear ODE
<br /> \left(2 r + f(r) f&#039;(r) \right) (1 + f&#039;(r)^2) + r f(r) f&#039;&#039;(r) = 0 <br />
subject to the initial conditions
<br /> f(R) = f(-R) = 0 \,.<br />
This problem is simpler than the one I actually want to solve, because in this case I know that the solution is
<br /> f(r) = (R^2 - r^2)^{1/2} \,. <br />

I would like to try and recreate the above solution by using NDSolve in mathematica. I try using the code

NDSolve[{(2 r + f[r] f'[r]) (1 + f'[r]^2) + r f[r] f''[r] == 0, 
  f[1] == 0, f[-1] == 0}, f, {r, -1, 1}]

but I receive the error message "Power::infy: Infinite expression 1/0. encountered." I would like to recreate the solution f(r) = \sqrt{1 - r^2}.

Thanks in advance for any help!

Steph

 

[Simon_Tyler]

An interesting question (and well asked). Unfortunately, I don't have a good answer for you.

If you use Trace[ NDSolve[...], TraceInternals->True], then you can see that NDSolve is trying the shooting method when it all goes wrong. However, I'm not sure what exactly is going wrong nor how to fix it.

I suggest you contact WRI tech support (http://www.wolfram.com/support/contact/) and see if they can sort it out.
If they do have a good answer, it would be great if you could post it here.