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Eigenmode problems/Boundary conditions at infinity?

• To: mathgroup at smc.vnet.net
• Subject: [mg69394] Eigenmode problems/Boundary conditions at infinity?
• From: AES <siegman at stanford.edu>
• Date: Sun, 10 Sep 2006 07:20:18 -0400 (EDT)
• Organization: Stanford University

Objective is to solve (numerically) a second-order differential equation 
in x containing one adjustable parameter so as to satisfy boundary 
conditions at x=0 and x=Infinity -- in other words, a classic eigenmode 
problem.

Any built-in Mathematica routines or packages for doing this? -- or does 
one have to gin up one's own version of the shooting method, or some 
other textbook method?

And, do any of Mathematica's equation solving routines handle boundary 
conditions at Infinity or "in the limit"? --  That is, "solution must 
approach zero as x approaches infinity".  Can't find any mention of this 
in the documentation, or in several of the standard Mathematica texts.