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