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