Frobenius method
Paul Abbott
the Frobenius method for obtaining the series solution to a general
linear second order differential equation in the neighborhood of a
regular singular point?
Of course, it is trivial to use Series and Solve to obtain solutions in
specific cases -- but I'd like something that handles all cases (such as
when the roots of the indicial equation differ by an integer).
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA 6907 mailto:pa...@physics.uwa.edu.au
AUSTRALIA http://www.physics.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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Peltio
Paul Abbott wrote in message <7b892k$4...@smc.vnet.net>...
>Does anyone have a Notebook which has a nice, general, implementation of
>the Frobenius method for obtaining the series solution to a general
>linear second order differential equation in the neighborhood of a
>regular singular point?
Talking about coincidences...
I just finished tinkering with a package that allows me to exert a control
over infinite sums.
This tiny package allows simplification, reindexing and derivation of
expressions (such as equations) containg object of type Summa (instead of
Sum, that is subject to simplifications not easily controllable by the
user). The type Summa[el,{n,n1,n2}] Reduces to Sum whenever both n1 and n2
are numerical.
I developed this package on version 2.2.1 but it works fine, I've been told,
on 3.0 : moreover, since the format is the same as that of Sum the
espressions obtained are quite cute on the new version.
I used this package to perform the substitutions of coefficients and
functions in a general second order equation and I came up with the indicial
equation (in symbolic form). When used with a particular equation, such as
the Bessel or the hypergeometric equations, I end up with the recursion
relations for a[n].
I have not implemented, though, any method to automatise the Frobenius
Method (specifically to find the second indipendent solution in
case of identical or integer separated roots, which requires some crafty
simplification),
but
if this package may be of some help, let me know and I'll send it to you,
along with a few examples (I had Mathematica do most of Abell and
Braselton's "Differential Equations w M 1st Ed" symbolic calculations of
chapters 6 and 7). I just have to translate the commands and the usage
message in English,thing I could gladly do as soon as I can.
(At no fee ; ) of course)
Regards,
Peltio
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