Re: "Solve[x==Erf[x], x]"
- To: mathgroup at smc.vnet.net
- Subject: [mg16511] Re: [mg16463] "Solve[x==Erf[x], x]"
- From: Markus van Almsick <m.van.almsick at cityweb.de>
- Date: Tue, 16 Mar 1999 03:59:56 -0500
- Sender: owner-wri-mathgroup at wolfram.com
Dear Matthias Tomann,
concerning:
>When I enter this equation, mathematica tells me:
>"Solve:tdep: The equations appear to involve transcendental functions of
>the variables in an essentially non-algebraic way."
>
>Can you tell me how to get around this problem an solve equations like
>x = 1 - Erf [x]
the Solve:tdep-warning pops up for mathematical reasons.
There is not algebraic solution to the equation. It's so-called transcendental.
Another example is x == Cos[x].
You have to solve the equation numerically.
1. See how the left side of your eqn compares to the right side by
plotting
Plot[{x , 1 - Erf[x]},{x,-3,3}]
2. Then use FindRoot to solve it:
FindRoot[x == 1 - Erf[x],{x,0.5}]
One could approach this problem using Taylor series:
Series[1-x-Erf[x],{x,0,10}]
InverseSeries[%]
Normal[%] /. x-> 0
Simplify[%]
N[%]
Good luck,
Markus van Almsick
http://www.wolfram.com/training/companies/almsick.html