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Advanced nonlinear integro-differential equation
*To*: mathgroup at smc.vnet.net
*Subject*: [mg70869] Advanced nonlinear integro-differential equation
*From*: Robert Berger <rberger06 at sinh.us>
*Date*: Mon, 30 Oct 2006 05:32:49 -0500 (EST)
*Organization*: EUnet Telekommunikationsdienstleistungs GmbH
Dear Mathematica experts! :-)
At the moment I'm dealing with the following nonlinear
integro-differential equation arising from a quantum
mechanic problem
y''[x] + 2 y'[x]/x + 2 y[x] = A (1 + B/x) y[x] f[x]
where
f'[x] = x^2 y[x] .
If the right sight of the equation is small, e.g., A = 0,
then the solution (linearized theory) is
y[x] = (C1 Sin[Sqrt[2] x] + C2 Cos[Sqrt[2] x])/x .
However, the problem is that in my case is A=1E-36, B=7.3E-3,
and y[0] = 1E26 (!) and therefore the nonlinear term is not
negligible. :-(
In this conjunction I have the following two questions:
1. Three boundary conditions are necessary.
It is easy to introduce y[0] = 1E26 and y'[0] = 0 as
boundary conditions in NDSolve but how can I use the
additional condition f[Infinity] = A?
2. It seems that the large y[0]-value cause some serious
numerical problems. Has anyone some tips, links, etc.
how to the rid of these problems?
Thanks!
Kindly regards,
Robert.
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