Why is this not working

Trying to solve 9 equtions 9 unknowns.

function [F] = MyFunc(x);

F = zeros(9,1);

x0 = [200, 150, 100, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5];

F(1) = 300 - x(1) - 50000*x(4).^2;

F(2) = x(1) - x(2) - 50000*x(5).^2;

F(3) = x(1) - x(3) - 50000*x(6).^2;

F(4) = x(2) - x(3) - 25000*x(7).^2;

F(5) = x(2) - 100 - 50000*x(8).^2;

F(6) = x(3) - 100 - 50000*x(9).^2;

F(7) = 0.04*x(4) - 0.01*x(5) - 0.01*x(6);

F(8) = 0.01*x(5) - 0.01*x(8) - 0.04*x(7);

F(9) = 0.01*x(6) + 0.04*x(7) - 0.01*X(9);

x = fsolve(@MyFunc,x0);

end

Answer 1

[Star Strider]

First, it appears that you are trying to solve it inside the functions, and that won’t work.

Second, this:

F(9) = 0.01*x(6) + 0.04*x(7) - 0.01*X(9);
                                    ↑ ← HERE

MATLAB is case-sensitive, so ‘x’ and ‘X’ are different.

This works:

function [F] = MyFunc(x);
F = zeros(9,1);
 
F(1) = 300 - x(1) - 50000*x(4).^2;
F(2) = x(1) - x(2) - 50000*x(5).^2;
F(3) = x(1) - x(3) - 50000*x(6).^2;
F(4) = x(2) - x(3) - 25000*x(7).^2;
F(5) = x(2) - 100 - 50000*x(8).^2;
F(6) = x(3) - 100 - 50000*x(9).^2;
F(7) = 0.04*x(4) - 0.01*x(5) - 0.01*x(6);
F(8) = 0.01*x(5) - 0.01*x(8) - 0.04*x(7);
F(9) = 0.01*x(6) + 0.04*x(7) - 0.01*x(9);
end

x0 = [200, 150, 100, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5];
x = fsolve(@MyFunc,x0)'

and produces:

x =
          277.777777777778
          188.888888888889
          188.888888888889
        0.0210818510677892
        0.0421637021355784
        0.0421637021355784
      2.57436435034422e-19
        0.0421637021355784
        0.0421637021355784

Answer 2

[Alex Sha]

There are another five more solutions:

No.	x1	x2	x3	x4	x5	x6	x7	x8	x9
1	300	200	200	0	0.0447213595499958	-0.0447213595499958	3.07555837662612E-68	0.0447213595499958	-0.0447213595499958
2	300	200	200	0	-0.0447213595499958	0.0447213595499958	1.27131391300829E-57	-0.0447213595499958	0.0447213595499958
3	299.975612730155	206.230947445434	193.744665284721	-0.000698387712451196	0.0433000381719742	-0.046093589021779	0.0223484067984383	-0.0460935890217791	0.0433000381719743
4	299.975612730155	206.230947445434	193.744665284721	0.000698387712451196	-0.0433000381719742	0.046093589021779	-0.0223484067984383	0.0460935890217791	-0.0433000381719743
5	277.777777777778	188.888888888889	188.888888888889	-0.0210818510677892	-0.0421637021355784	-0.0421637021355784	4.53008323503054E-19	-0.0421637021355784	-0.0421637021355784