Date: Nov 28, 2012 6:47 AM
Author: Leslaw Bieniasz
Subject: analytical ODE solution (a bit off-topic)



Hi,

I need to solve analytically a certain second order ODE,
which takes the general form

y''(x) - p(z,x)*y(x) = 0.

where p(z,x) is a polynomial and y(x) is to be determined. The polynomial
depends on a complex parameter z.

The problem is that I need a possibly approximate but analytical solution,
perhaps in the form of some truncated series (but not the series in powers
of x), not just numerical values of the solution.

Are there any techniques available? Some kind of
successive approximations that really work (are convergent)?
Someone has suggested to me the WKB approximation, but I think
it is not suitable, because the above equation is not singularly
perturbed.

Leslaw