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