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Re: Solving simple equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83225] Re: Solving simple equations
  • From: Bill Rowe <readnewsciv at sbcglobal.net>
  • Date: Thu, 15 Nov 2007 05:42:43 -0500 (EST)

On 11/14/07 at 4:51 AM, hredlich at gmx.net (Holger) wrote:

>I'm trying to solve these two simple equations but it doesn't work.
>
>meqn = { x'[t]==beta(x[t]+(Subscript[P,f]-p[t])),
>p'[t]==(Tanh[Subscript[a,1](x[t]+(Subscript[P,f]-p[t]))+
>Subscript[a,2]x[t]]-x[t])
>};

>eqp = NSolve[ meqn/.{ p'[t]->0,x'[t]->0},{p[t], x[t]
>}
>]

>I guess I'm doing a mistake somewhere. Does anyone have idea where
>the mistake is?

You are trying to get NSolve to do something it simply isn't
intended to do. NSolve is intended to provide a numerical
solution to a set of polynomial equations. Your equations cannot
be reduced to polynomials and you've not given numeric values to
all of the coefficients.

You can solve things with Mathematica as follows:

=46irst, lets simplify things a bit by getting rid of the unneeded
variable t, i.e. (This needs to be done if you are going to get
a numeric solution)

In[5]:= meqn /. {p'[t] -> 0, x'[t] -> 0, p[t] -> p, x[t] -> x}

Out[5]= {0 == beta*(-p + x + Subscript[P, f]),
    0 == Tanh[x*Subscript[a, 2] + Subscript[a, 1]*
              (-p + x + Subscript[P, f])] - x}

Now the first equation can easily be solved for p

In[6]:= Solve[First[%], p]

Out[6]= {{p -> x + Subscript[P, f]}}

putting this solution into the second equation gives

In[7]:= Last[%%] /. First[%]

Out[7]= 0 == Tanh[x*Subscript[a, 2]] - x

Now once Subscript[a, 2] is replaced with a specific numeric
value, FindRoot can be used to find a numeric solution for x.
That can then be substituted into the solution to the first
equation to get p.
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