MathGroup Archive 1999

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: "Solve[x==Erf[x], x]"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg16499] Re: [mg16463] "Solve[x==Erf[x], x]"
  • From: BobHanlon at aol.com
  • Date: Tue, 16 Mar 1999 03:59:49 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 3/13/99 9:51:50 AM, tomann at k4.hhl.de writes:

>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]
>

Matt,

Plot[x - 1 + Erf[x], {x, 0, 1}];

The root is in the vicinity of 0.5

FindRoot[x == 1 - Erf[x], {x, 0.5}]

{x -> 0.4891163447388041}

FindMinimum[(x - 1 + Erf[x])^2, {x, .5}][[2]]

{x -> 0.4891163449110946}

Solve would work to determine an approximate value, if you first 
approximate the function with a polynomial:

Select[Solve[Normal[Series[x - 1 + Erf[x], {x, 0.5, 4}]]==0, 
    x], ((Abs[x-0.5] /. #) < .1)&]

{{x -> 0.4891163449134484}}


Bob Hanlon


  • Prev by Date: Re: StartingParameters
  • Next by Date: An open letter
  • Previous by thread: "Solve[x==Erf[x], x]"
  • Next by thread: Re: "Solve[x==Erf[x], x]"