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Solvability sensitive to small changes in numerical input

• To: mathgroup at smc.vnet.net
• Subject: [mg47494] Solvability sensitive to small changes in numerical input
• From: "Gareth J. Russell" <gjr2008 at columbia.edu>
• Date: Wed, 14 Apr 2004 07:16:48 -0400 (EDT)
• Organization: Columbia University
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

I have a function that includes the Solve command

f[a1_, a2_, b_] := Module[{c},
    
    c = 2*b/(b - 1);
    
    Solve[b/(1 + (a1*n)^c) + b/(1 + (a2*n)^c) == 2, n]
    
]    ]

but it seems very sensitive to the numerical input. For example,

f[2., 0.05, 6.19]

and

f[2., 0.05, 6.21]

Produce the error "The equations appear to involve the variables to be 
solved for in an essentially non-algebraic way."

Whereas

f[2., 0.05, 6.20]

produces the solutions

{{n -> -23.8725 - 13.2503i]}, {n -> -23.8725 + 13.2503i}, {
  n -> 0.183281 - 0.707873i}, {n -> 0.183281 + 0.707873i]}, {n -> 27.
3032}}

Can anyone enlighten me as to what is going on here? Other peoples' work 
suggests that, given a1 = 2., it should be possible to get numerical 
solutions for a large range of values of a2 and b.

If it makes a differences we make the assumptions a1 > 0, a2 > 0, a2 < 
a1 and b >= 1.

Oh, and v5.0.1.0 on Mac OS X

Thanks!

Gareth Russell

Columbia University

• Follow-Ups:
  • Re: Solvability sensitive to small changes in numerical input
    • From: Oleksandr Pavlyk <pavlyk@phys.psu.edu>
  • Re: Solvability sensitive to small changes in numerical input
    • From: Daniel Lichtblau <danl@wolfram.com>