fsolve (nonlinear) equation solver with given one equation.

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Sun Kyoo Choi
Sun Kyoo Choi 2020-3-6
编辑： Ameer Hamza 2020-3-6
How could I solve the equation, using fsolve? Currently, I do have p4, p1, r4, r1, a1, and a4 values, but I am trying to find p2/p1.
It does not have to be fsolve. Any methods it can solve is fine.

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回答（1 个）

Ameer Hamza
Ameer Hamza 2020-3-6
You can use fzero.
Since you already know the values of p1, p4, r1, r4, a1, and a4, you can use solve the equation for the value of p2 to get . For example,
% dummy values
p1 = 1;
p4 = 2;
r1 = 1;
r4 = 2;
a1 = 1;
a4 = 1;
fun = @(p2) p2/p4*(1 -((r4-1)*a1/a4*(p2/p1-1))./(2*r1*(2*r1+(r1+1)*(p2/p1-1))).^.5).^(-2.*r4./(r4-1))-1;
result = fzero(fun, 10)/p1;
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Sun Kyoo Choi
Sun Kyoo Choi 2020-3-6
For example, if my p4 = 29.82, p1 = 6.78, r1=r4=1.4, a1=a4=96.13, what would be p2?
Also, in result, result = fzero(fun, 10)/p1, what does 10 represent?
Would it be okay to use any value for that?
Thank you for your answer.
Ameer Hamza
Ameer Hamza 2020-3-6
编辑：Ameer Hamza 2020-3-6
Here, p2 = fzero(fun, 10) and therefore result = p2/p1.
10 is the initial estimate of the value of p1. It is used as a starting point by the solving algorithm. You can use any value, but you will get a better solution if it is near the actual solution. You can use your knowledge about the problem to give a rough estimate of its optimal value.

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