Re: Shooting for the endpoint of a ODE system
- To: mathgroup at smc.vnet.net
- Subject: [mg121154] Re: Shooting for the endpoint of a ODE system
- From: Alois Steindl <Alois.Steindl at tuwien.ac.at>
- Date: Wed, 31 Aug 2011 07:41:05 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <j3l18c$bu5$1@smc.vnet.net>
Hello,
there is a nice article on such problems:
@ARTICLE{Asher:Russell:81,
Author = {U. M. Asher and R. D. Russell},
Title = {Reformulation of boundary value problems into
standard form},
Journal = {SIAM Review},
volume = 23,
pages = {238 - 254},
year = 1981,
}
In your case the standard trick to scale the independent variable should
work:
Set x= xi*X, with X the unknown length, and xi in [0, 1].
Then your original differential equation
dy/dx=f(x, y)
becomes
dy/dxi=X*f(xi*X, y)
dX/dxi=0
Good luck
Alois
--
Alois Steindl, Tel.: +43 (1) 58801 / 32558
Inst. for Mechanics and Mechatronics Fax.: +43 (1) 58801 / 32598
Vienna University of Technology, A-1040 Wiedner Hauptstr. 8-10