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Tricky differential equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41469] Tricky differential equation
  • From: Luiz Melo <luiz.melo at polymtl.ca>
  • Date: Wed, 21 May 2003 08:02:31 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello everyone,

I'm trying to find the numerical solution of the following
differential equation (r is the independent variable):

x''[r] + 1/r x'[r] + (p - 1/r^2)*Sin[x[r]]*Cos[x[r]] == 0 ,

with boundary conditions: x'[1] == 0 , and x[0] -> "has to be finite",

but I'm having at least two problems:

1) I don't know how to submit the BC "finite" to Mathematica;
2) The coefficient p is about 10^4. For this reason, it seems
that the Runge-Kutta method usually used for numerical
integration of ordinary differential equations turns out
to be unsuccessfull in our case. Do we need a special method
to solve this?

The solution of this equation gives the internal magnetic structure
of a cylinder. The function x[r] is the angle between the
magnetization and the axial direction, and it depends on the radial
direction, r.

I would like to plot the Cossine of the result as a function of r
(which varies from 0 to 1), for several values of p.

Any help will be very appreciated!
Thank you

Luiz Melo

Ecole Polytechnique de Montreal,
Montreal, Quebec
luiz.melo at polymtl.ca




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