[Date Index]
[Thread Index]
[Author Index]
Re: Please help: How to use Mathematica to get Parametric solution for a transcendental equation?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg69335] Re: Please help: How to use Mathematica to get Parametric solution for a transcendental equation?
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Thu, 7 Sep 2006 04:30:42 -0400 (EDT)
*Organization*: The University of Western Australia
*References*: <edjhha$lvs$1@smc.vnet.net>
In article <edjhha$lvs$1 at smc.vnet.net>, Leonxf <leonxf at gmail.com>
wrote:
> The function is just one:
>
> A*(1+G)+a*[(1+G)^t]=T, where A,a,t,T are all positive real numbers, and t is
> no larger than 1.
Consider the equivalent transcendental equation
a g + b g^t == c
where a > 0, b > 0, c > 0, 0 < t <= 1, and you want to find g.
Using series reversion:
http://mathworld.wolfram.com/SeriesReversion.html
one obtains a series expansion of the solution (about g == 1 to 2nd
order):
ser = InverseSeries[ Series[ a g + b g^t, {g, 1, 2}], c ]
2 2
(-a - b + c) (b t - b t ) (-a - b + c) 3
1 + ------------ + -------------------------- + O[-a - b + c]
a + b t 3
2 (a + b t)
One can choose a different expansion point and compute to higher order.
For, say, a -> 3, b -> 1, c -> 2.5 and t -> 0.7 one obtains
Normal[ser]/. {a -> 3, b -> 1, c -> 2.5, t -> 0.7}
0.5992586816180681
Using FindRoot, one obtains
FindRoot[a g+b g^t == c /. {a -> 3, b -> 1, c -> 2.5, t -> 0.7}, {g, 1}]
{g -> 0.600165573071457}
Cheers,
Paul
_______________________________________________________________________
Paul Abbott Phone: 61 8 6488 2734
School of Physics, M013 Fax: +61 8 6488 1014
The University of Western Australia (CRICOS Provider No 00126G)
AUSTRALIA http://physics.uwa.edu.au/~paul
Prev by Date:
**Re: repost -Difficulties with xml**
Next by Date:
**Re: Why doesn't Mathematica solve this simple differential equation?**
Previous by thread:
**Re: Re: Please help: How to use Mathematica to get Parametric solution for a transcendental equation?**
Next by thread:
**RE: Mathmatica StyleSheet questions**
| |