Advanced nonlinear integro-differential equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg71044] [mg70869] Advanced nonlinear integro-differential equation*From*: Robert Berger <rberger06 at sinh.us>*Date*: Mon, 6 Nov 2006 02:52:52 -0500 (EST)

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.