Solve nonlinear equation with positive solution (fsolve)

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Benjamin Wodey 2018-6-7

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评论： Benjamin Wodey 2018-6-8

Hello, I would like to solve 3 non linear equation:

F(1) = 0.44*x(1) + 0.23*x(2) + 0.33*x(3) - 5140;

F(2) = 0.23*x(1) + 0.44*x(2) + 0.33*x(3) - 4970;

F(3) = 4*(0.44 + 0.23)*(x(1)*x(2)/(3*x(2)+x(1))) + 0.33*x(3) - 4380;

Here, x is 3 different young modulus and my problem is, using fsolve give me negative values... Do you know if it's possible to find positive values or should I try another way ?

Thank for yours answers

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sloppydisk 2018-6-7

I assume you're setting each of the three expressions to zero?

Benjamin Wodey 2018-6-7

right!

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Answer 1

sloppydisk 2018-6-7

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You can set an assumption on the equations using assume, in this case there seem to be no solutions for this problem.

x = sym('x', [3 1]);
F(1) = 0.44*x(1) + 0.23*x(2) + 0.33*x(3) - 5140==0;
F(2) = 0.23*x(1) + 0.44*x(2) + 0.33*x(3) - 4970==0;
F(3) = 4*(0.44 + 0.23)*(x(1)*x(2)/(3*x(2)+x(1))) + 0.33*x(3) - 4380==0;
assume(x>=0)
sol1 = solve(F, x)

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Benjamin Wodey 2018-6-8

okay, so maybe I have to find other equations to solve my problem

thank you for your answer

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Answer 2

Star Strider 2018-6-7

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https://ww2.mathworks.cn/matlabcentral/answers/404563-solve-nonlinear-equation-with-positive-solution-fsolve#answer_323691

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I am not certain what the values of ‘x’ should be.

Try these:

fcn = @(x) [0.44*x(1) + 0.23*x(2) + 0.33*x(3) - 5140;  0.23*x(1) + 0.44*x(2) + 0.33*x(3) - 4970;  4*(0.44 + 0.23)*(x(1)*x(2)/(3*x(2)+x(1))) + 0.33*x(3) - 4380];
[xs,fv] = fsolve(@(x) norm(fcn(x)), [1; 1; 1])
[xs,fv] = fmincon(@(x) sum(fcn(x)), [1; 1; 1], [], [], [], [], [0; 0; 0],[1; 1; 1]*Inf)

The first one provides a sort of ‘pseudo-constraint’ using the norm of the output. The second uses fmincon to constrain the parameters, however since it requires that the argument function return a scalar, leaves that as a problem for you to solve. (I arbitrarily chose to sum them here.)