Re: Beginner--Help on using FindRoot to solve the system of equations

• To: mathgroup at smc.vnet.net
• Subject: [mg66225] Re: Beginner--Help on using FindRoot to solve the system of equations
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 4 May 2006 05:21:34 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <e39kql\$cud\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```xiaochu at che.utexas.edu wrote:
> This is a code to solve vapor-liquid equilibrium by van der Waals Equation of State.
>
>
>
> (* Name of EOS *)
>
> EOSName = "Van der Waals";
>
> Ttilde = .;
>
> Dtilde = .;
>
> Z = 3/(3-Dtilde)-9*Dtilde/8/Ttilde;
>
> (* Related variables *)
>
> Psi1 = (-9*Dtilde)/(8*Ttilde) - Log[3-Dtilde];
>
> lnB = (1-Z)-Psi1;
>
> mu = -lnB+Log[Dtilde];
>
> P = Dr Ttilde Z;
>
> DtildeG=10^-14;
>
> DtildeL=2.91;
>
> Dtilde1=.;
>
> Dtilde2=.;
>
> mu1=mu/.Dtilde->Dtilde1;
>
> mu2=mu/.Dtilde->Dtilde2;
>
> P1=P/.Dtilde->Dtilde1;
>
> P2=P/.Dtilde->Dtilde2;
>
> Ttilde = 0.1;
>
> Result=
>     	FindRoot[
>       		{P1==P2,mu1==mu2},
>       		{Dtilde1,DtildeG},
>       		{Dtilde2,DtildeL},
>       		MaxIterations->1000,
>       		WorkingPrecision->16];
>
> Link to the forum page for this post:
> http://www.mathematica-users.org/webMathematica/wiki/wiki.jsp?pageName=Special:Forum_ViewTopic&pid=10101#p10101
> Posted through http://www.mathematica-users.org [[postId=10101]]
>
>
Hi,

Use exact values for your parameters, say, 291/100 rather than 2.91.
The parameter Dr that occurs in the definition of P has no value when
feeding *FindRoot*. Since *FindRoot* is looking for numerics answers
only, every parameter must have a value, otherwise it must be listed has
variable (below, I have chosen arbitrarily the value 1 for Dr).

In[1]:=
EOSName = "Van der Waals";
Ttilde =. ;
Dtilde =. ;
Z = 3/(3 - Dtilde) - 9*(Dtilde/(8*Ttilde));
Psi1 = (-9*Dtilde)/(8*Ttilde) - Log[3 - Dtilde];
lnB = (1 - Z) - Psi1;
mu = -lnB + Log[Dtilde];
P = Dr*Ttilde*Z;
DtildeG = 10^(-14);
DtildeL = 291/100;
Dtilde1 =. ;
Dtilde2 =. ;
mu1 = mu /. Dtilde -> Dtilde1;
mu2 = mu /. Dtilde -> Dtilde2;
P1 = P /. Dtilde -> Dtilde1;
P2 = P /. Dtilde -> Dtilde2;
Ttilde = 1/10;
Result = FindRoot[{P1 == P2, mu1 == mu2} /. Dr -> 1,
{{Dtilde1, DtildeG}, {Dtilde2, DtildeL}},
MaxIterations -> 1000, WorkingPrecision -> 16]

Out[18]=
{Dtilde1 ->
5.8774260468984207185228791`15.999999999999998*^-13\
, Dtilde2 -> 2.9111111111110937621138592336`16.}

HTH,
Jean-Marc

```

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