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MathGroup Archive 2004

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FindRoot and dealing with small numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47025] FindRoot and dealing with small numbers
  • From: criticalheat at web.de (criticalheap)
  • Date: Mon, 22 Mar 2004 05:18:34 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

I have got a problem concerning calculation with small numbers.

I want to solve an equation of the following kind:

equation := x - g(b) - f(x,b) == 0 

and I want to plot the function h(b) = x, as a function of the
parameter b.

I use the following syntax:

FindRoot[equation , {x, {- 10^(-25), 10^(-30)}}, AccuracyGoal -> 15, 
  WorkingPrecision -> 16, MaxIterations -> 5000]

solnumerical := x /. % 
N[solnumerical]

Now I have got 2 problems:

i) The line solnumerical := x /. % gives the error line:

ReplaceAll::"reps": "\!\({Null}\) is neither a list of replacement
rules nor \
a valid dispatch table, and so cannot be used for replacing."

ii) How can I teach mathematica to calculate with such small numbers.
He cuts every
number after the sixth decimal, which leads to wrong numerical
results.
for example hbar = 1.054571596 10^(-34) OUTPUT: (1.05457 10^-34) where
are the last digits ?



Thanks for your comment, Peter


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