NDSolve and partial differential equations
- To: mathgroup at smc.vnet.net
- Subject: [mg42339] NDSolve and partial differential equations
- From: AES/newspost <siegman at stanford.edu>
- Date: Tue, 1 Jul 2003 08:45:44 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
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?