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Sunanda Lakkimsetti

How to find the intersection point of four equations?

Sunanda Lakkimsetti
Posted 7 months ago
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Hi, I have four equations of four variables. I defined the range of the four variables and I need to find the intersection of the four equations in the given range. The equations are in terms of the four variables. Can you please tell me how to find the intersection?

Y2 =.;
Y3 =.;
l2 =.;
l3 =.;
Y1 = 0.0125;
l1 = 0.0108366;
lambda = {0.043656,0.0410959,0.0413712,0.0433463,0.0423413};
b1 = 0.0502519;
b3 = 0.0161692;
t21 = ((2*Pi)/lambda[[1]])*l2;
t31 = ((2*Pi)/lambda[[1]])*l3;
t23 = ((2*Pi)/lambda[[5]])*l2;
t33 = ((2*Pi)/lambda[[5]])*l3;
t11 = ((2*Pi)/lambda[[1]])*l1;
t13 = ((2*Pi)/lambda[[5]])*l1;
Manipulate[t21 = (2*Pi/lambda[[1]])*l2;
t31 = (2*Pi/lambda[[1]])*l3;
t23 = (2*Pi/lambda[[5]])*l2;
t33 = (2*Pi/lambda[[5]])*l3; 
plot = Plot[{2*Y1*Tan[t11] + Y2*Tan[t21] + Y3*Tan[t31], 
2*Y1*Tan[t13] + Y2*Tan[t23] + Y3*Tan[t33], 
t11*Y1 + t21*(Y2/2)*(Sec[t21]^2/Sec[t11]^2) + 
 t31*(Y3/2)*(Sec[t31]^2/Sec[t11]^2) - b1, 
t13*Y1 + t23*(Y2/2)*(Sec[t23]^2/Sec[t13]^2) + 
 t33*(Y3/2)*(Sec[t33]^2/Sec[t13]^2) - b3},
{Y3, 0.008, 0.05}],
{Y2, 0.008, 0.05}, {l3, 0.008, 0.012}, {l2, 0.008, 0.012}]
POSTED BY: Sunanda Lakkimsetti
Answer
13 Replies
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The code doesn't work for me ?
POSTED BY: Mariusz Iwaniuk
Answer

The range can be increased by {Y9,0.008,0.05}, {Y2,0.008,0.05},{l33,0.008,0.012},{l22,0.008,0.012}. Any problem with the code? Its working fine for me. Please let me know.
POSTED BY: Sunanda Lakkimsetti
Answer
Rohit Namjoshi
Rohit Namjoshi
Posted 7 months ago

There are several undefined symbols in the code, t11, t21, t13 ....
POSTED BY: Rohit Namjoshi
Answer

Please check the edited code.
POSTED BY: Sunanda Lakkimsetti
Answer

The code doesn't work for me, with fresh kernel? Update the code.

What is that: 

  Y2 =.;

?
POSTED BY: Mariusz Iwaniuk
Answer
Rohit Namjoshi
Rohit Namjoshi
Posted 7 months ago

Hi Mariusz,

=. is syntax for Unset.
POSTED BY: Rohit Namjoshi
Answer

I defined it as a variable.
POSTED BY: Sunanda Lakkimsetti
Answer
Rohit Namjoshi
Rohit Namjoshi
Posted 7 months ago

t11 is still missing.
POSTED BY: Rohit Namjoshi
Answer

Sorry. Updated the code.

POSTED BY: Sunanda Lakkimsetti
Answer
Rohit Namjoshi
Rohit Namjoshi
Posted 7 months ago

There are still undefined symbols. Execute the latest code against a new kernel.
POSTED BY: Rohit Namjoshi
Answer

Please check the updated code.
POSTED BY: Sunanda Lakkimsetti
Answer

Why do you believe there is a simultaneous zero in those ranges of the variables? FindRoot and FindMinimum fail to locate any zero. And the Manipulate does not indicate likelihood of such either, as best I can tell.
POSTED BY: Daniel Lichtblau
Answer

It'll not be an exact zero but its a very small value of the order of 10^(-29). I need to find the values of the 4 unknowns from the plot. I guess the solution gets trapped in local minima.
POSTED BY: Sunanda Lakkimsetti
Answer
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