Re: NDSolve and partial differential equations
- To: mathgroup at smc.vnet.net
- Subject: [mg42354] Re: NDSolve and partial differential equations
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Wed, 2 Jul 2003 06:36:16 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <bds0s0$64t$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
at least a consistent boundary condition for x
should be added.
Regards
Jens
AES/newspost wrote:
>
> The paraxial wave equation for an optical beam propagating in the z
> direction is in essence
>
> D[ f[x, z], z] = I alpha D[ f[x,z], {x,2}]
>
> I'd like to integrate this forward in z starting with some specified
> input profile f[x,0] at z = 0. Approaches of the general form
>
> NDSolve[ { D[ f[x, z], z] == I alpha D[ f[x, z], {x,2}],
> f[x, 0] == Exp[-x^2]}, {x,-5,5}, {z,0,2}]
>
> and variations on this theme are giving me a lot of mysterious error
> messages.
>
> Is there a way to do this?