RE: Q: Weber equation
- To: mathgroup at smc.vnet.net
- Subject: [mg9771] RE: [mg9701] Q: Weber equation
- From: Jean-Marie THOMAS <jmthomas at cybercable.tm.fr>
- Date: Tue, 25 Nov 1997 00:07:21 -0500
- Sender: owner-wri-mathgroup at wolfram.com
The trouble in your equation comes from the fact that your boundary
conditions for x=1 conflict with the series developpment in x=0. You
then have to use Normal in order to replace your series by a
polynomial:
\!\(w[x_] = Sum[a[i] x\^i, {i, 0, 6}] + O[x]\^7\)
\!\(eq = \(b\^2\) D[w[x], {x, 2}] - \((x\^2/4 + b/2 + a)\) w[x] == 0 &&
w[0] == 1\)
le1=LogicalExpand[eq]
sle1=Solve[le1,Table[a[i],{i,0,6}]]
(*this will give only partial solutions*)
wn[x_]=Normal at First[w[x]/.sle1]
eq2=wn'[1]+wn[1] d (1/2+b/2)==0
sle2=Solve[eq2,a[3]]
wnn[x_]=wn[x]/.First at First@sle2
Plot[Evaluate[wnn[x]/.{a->Random[],b->Random[],c->Random[],d->Random[]}]
,{x,0,
2}]
I don't believe the choice of the order for this series is judicious,
let's pretend it's a start for more precise investigations.
Hope this helps,
----------------------------------------------- Jean-Marie THOMAS
Conseil et Audit en Ingenierie de Calcul jmthomas at cybercable.tm.fr
+33 (0)3 88 32 93 64
www.cybercable.tm.fr/~jmthomas
=======================
-----Message d'origine-----
De: Boguslaw Ptaszynski [SMTP:ptaszyns at galaxy.uci.agh.edu.pl]
Date: vendredi 21 novembre 1997 07:32 A: mathgroup at smc.vnet.net
Objet: [mg9701] Q: Weber equation
Hi,
I have a problem with a Weber equation and boundary conditions: b^2
w''[x] - (x^2/4 + b/2+ a) w[x]==0 Weber equation (b,a -constans)
w[x=0]==1
w'[x=1]+ w[x=1] d (1/2+b/2) == 0
I want to solve this problem in Mathematica3,0 under Windows 95 . I have
solved this but in form very complcated series. Maybe is somebody who
know how solve this in simply form?
THANKS,
Boguslaw Ptaszynski