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