Mathematica 9 is now available
Student Support Forum
-----
Student Support Forum: 'Solve nonlinear algberic euations' topicStudent Support Forum > General > "Solve nonlinear algberic euations"

< Previous CommentHelp | Reply To Comment | Reply To Topic
Author Comment/Response
Bill Simpson
07/10/13 4:35pm

In Response To 'Re: Re: Solve nonlinear algberic euations'
---------
I did not get the "cannot solve with methods" error that you did. Perhaps my version is different.

Can you use this to solve for three of your variables and then substitute the results into a smaller problem to solve for the rest?

In[1]:= \[Rho]0 = 127/100;
p0 = 1013*10^2;
p1 = 3*p0;
\[Gamma] = 14/10;
\[Phi]1 = 30*(Pi/180);
Simplify[Reduce[{
\[Rho]0*u0*Sin[\[Phi]1] == \[Rho]1*u1*Sin[\[Phi]1 - \[Theta]1],
\[Rho]1*u1*Sin[\[Phi]2] == \[Rho]2*u2*Sin[\[Phi]2 - \[Theta]1],
p0 + \[Rho]0*(u0*Sin[\[Phi]1])^2 == p1 + \[Rho]1*(u1*Sin[\[Phi]1 - \[Theta]1])^2, p1 + \[Rho]1*(u1*Sin[\[Phi]2])^2 == p2 + \[Rho]2*(u2*Sin[\[Phi]2 - \[Theta]1])^2,
\[Gamma]*(p0/((\[Gamma] - 1)*\[Rho]0)) + (1/2)*(u0*Sin[\[Phi]1])^2 == \[Gamma]*(p1/((\[Gamma] - 1)*\[Rho]1)) + (1/2)*(u1*Sin[\[Phi]1 - \[Theta]1])^2,
\[Gamma]*(p1/((\[Gamma] - 1)*\[Rho]1)) + (1/2)*(u1*Sin[\[Phi]2])^2 == \[Gamma]*(p2/((\[Gamma] - 1)*\[Rho]2)) + (1/2)*(u2*Sin[\[Phi]2 - \[Theta]1])^2
}, {u0, u1, u2}]]

Out[6]= ...LargeResultSnipped...

The result is large and complicated, but there are some repeated items and you might be able to use information you have about your angles being Real and other information to obtain small values for your variables.

If you have any additional information about the domain of any of your variables then this might help, but sometimes that information will make Reduce slower.

URL: ,

Subject (listing for 'Solve nonlinear algberic euations')
Author Date Posted
Solve nonlinear algberic euations Ritwik Ghoshal 07/08/13 05:25am
Re: Solve nonlinear algberic euations Bill Simpson 07/08/13 4:56pm
Re: Re: Solve nonlinear algberic euations Ritwik Ghoshal 07/10/13 02:03am
Re: Re: Re: Solve nonlinear algberic euations Bill Simpson 07/10/13 4:35pm
< Previous CommentHelp | Reply To Comment | Reply To Topic