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Analytical ODE solving
Posted:
Nov 23, 2012 6:13 AM
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Hi,
I need to solve analytically a certain second order ODE
having the form
u''(x) - p(x)*u(x) = 0
where p(x) is a known polynomial. The ODE most likely does not
have a solution expressed by known analytical functions, so that
by "analytical solution" I mean a solution that can be
perhaps expressed by some series or maybe integral.
I have tried a power series solution, but this approach is
not useful for me for some reasons. Are there any other
approaches that might be applicable? Some kind of successive
approximations? Or other kinds of series solutions,
not by power series? Please direct me to the relevant literature
or web sites. I emphasise that I need to have a formula
for the general solution (without taking into account boundary
conditions), where all coefficients are given in an
analytical form and can be subject to analytical processing.
It's not sufficient for me just to compute the numerical values
for a particular set of boundary conditions.
Leslaw
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