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MathGroup Archive 1998

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Re: Re: ODE

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14529] Re: [mg14501] Re: [mg14443] ODE
  • From: "Jens-Peer Kuska" <kuska at linmpi.mpg.de>
  • Date: Thu, 29 Oct 1998 04:33:26 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Alessandro,

a) you can use the build in functions with

deqn=y''[x]-y'[x]/y[x]+(b-a*x)*y[x]==0

and
sorder=4;
Solve[LogicalExpand[
    deqn /.Thread[{#,D[#,x],D[#,x,x]} & /@ (

y[x]->Sum[C[i]*x^i,{i,0,sorder}]+O[x]^(sorder+1))]],Table[C[i],{i,2,sorder}]
]

you get the coefficients of the power series solution at x=0 as
functions
of C[0]=y[0] and C[1]=y'[1]. It is so simple that no package is
needed.

b) dealing with infinite series need a large amount of programming. For
infinite
    series solutions of *linear* look to the SpecialFunctions.m Package
from Wolfram Koepf, Axel Rennoch, Gregor Stoelting 1992, 1993
    Wolfram Koepf 1994, 1995, 1996. The package for linear deqn's is ca
270 kByte
   Mathematica code. For nonlinear equations no algorithm and/or package
exist.

Hope that helps
  Jens


-----Original Message-----
From: Ing. Alessandro Toscano Dr. <toscano at ieee.org> To:
mathgroup at smc.vnet.net
Subject: [mg14529] [mg14501] Re: [mg14443] ODE


I found that the ODE:

(A+B*x)*y(x) - y'(x)/y + y''(x)=

has an analytical, series solution near a regular singular point.

Is there any package or notebook which solves ODE in terms of the so
called series solutions?

If not, can you help me to perform the task of finding solutions of ODE
as an infinite series in powers of x?

Alessandro


***********************************
Ing. Alessandro Toscano Dr.

Universite di Roma Tre
Dip. Ingegneria Elettronica
Via della Vasca Navale, 84
00146, Roma, ITALIA

Tel. +39-6-55177095
Fax  +39-6-5579078
e-mail: a.toscano at uniroma3.it,
toscano at ieee.org

************************************




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