Re: solving non-algebraic exponential equations
- To: mathgroup at smc.vnet.net
- Subject: [mg38096] Re: [mg38059] solving non-algebraic exponential equations
- From: Tomas Garza <tgarza01 at prodigy.net.mx>
- Date: Tue, 3 Dec 2002 04:30:33 -0500 (EST)
- References: <200211281908.OAA23991@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Indeed, NSolve gives a list of numerical approximations to the roots of a
polynomial equation (cf. OnLine Help). Use instead FindRoot, and of course
you'll have to supply numerical values for a and b, as well as initial
values. This shouldn't be difficult if you begin by plotting your function
to see where to set initial values for the root finding process. For
example, if you define
In[1]:=
g[x_, a_, b_] := Exp[(-Pi)*(a/x)] + Exp[(-Pi)*(b/x)] - 1
and plot this function, say for a = 2.5 and b = 3.0, you'll find that the
root lies somewhere between 11 and 13:
In[2]:=
Plot[g[x, 2.5, 3.], {x, 1, 15}, PlotRange ->
{{8, 15}, {-1, 1}}];
Then use FindRoot:
In[3]:=
FindRoot[g[x, 2.5, 3.] == 0, {x, {11, 13}}]
Out[3]=
{x -> 12.428204959984097}
Tomas Garza
Mexico City
----- Original Message -----
From: "Eva Hohberger" <eva.hoehberger at gmx.net>
To: mathgroup at smc.vnet.net
Subject: [mg38096] [mg38059] solving non-algebraic exponential equations
> I am trying to solve the following equation for given values of two
> parameters a and b:
>
> NSolve[Exp[-Pi*a/x] + Exp[-Pi*b/x] == 1, x]
>
> This is straightforward for integer values of the parameters a and b
> (e.g. a=1, b=1). However, Mathematica is unable to compute the
> solution for non-integer values of a and b (e.g. a=1.1, b=1.1; even
> a=1.0, b=1.0 doesn't work). Instead, the error message "Solve::"tdep":
> "The equations appear to involve the variables to be solved for in an
> essentially non-algebraic way." is produced.
>
> Can anybody point out a way to overcome this problem and to obtain a
> solution?
>
> Thanks,
> Eva
>
>