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MathGroup Archive 2006

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Re: NDSolve with boundary condition(s) at infinity?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68531] Re: NDSolve with boundary condition(s) at infinity?
  • From: "Narasimham" <mathma18 at hotmail.com>
  • Date: Wed, 9 Aug 2006 04:18:42 -0400 (EDT)
  • References: <eb6kgc$nnh$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

AES wrote:
> Can NDSolve be used for ODEs with one (or two) boundary condition(s)
> being that solution must tend toward zero at infinity?
>
> [Eigenmodes of complex slab waveguides with transversely varying index
> and loss profiles being the case of interest.]
>
> Pointers to alternative Mathematica-based attacks?
>
> [Didn't find any answer to first query in extended documentation for
> NDSolve.]

If function behaviour is a priori known to have symmetry somewhere,
perhaps better to avoid asymmetric asymptotic boundary conditions in
the ODE itself. Otherwise I do not know.. For example in Gaussian
distribution y''[x]= - y[x] ( 1- ( x/a)^2 ), a choice of symmetric case
boundary conditions as initial value problem y[0] ==1 , y'[0] ==0
includes the zero at infinity automatically.


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