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