i need to solve 7 nonlinear equations with 7 unknows

G = 600:100:1200;
x0 = [300;300;300;300;300;300;300];
options = optimset('Display','off');
X(i) = NaN(1,length(G));
for i = 600:length(G)
    fsol = fsolve(@(x) solutionsproblem(x,G(i)),x0,options);
    X(i) = fsol(1);
end

function F = solutionsproblem(x,G)
Tg1 = 300;
Tg2 = 301.5;
Ta = 305.8;
Tl = 302;
Tf = 302;
Tb = 302;
Th = 300;
F(1) = 0.0425*G + 1.41*10^(-8)*x(2)^(4) + 1.34*x(2) - 9.12*10^(-9)*x(1)^(4) + 341 - 2402.77*x(1) + 2400*Tg1;
F(2) = 0.0204*G - (3.48*10^(-8) + 4.35*10^(-10)*1)*x(2)^(4) + 1.41*10^(-8)*x(1)^(4) + 8.01*10^(-11)* x(4)^(4) + 2.43*10^(-8)*x(3)^(4) + 4.35*10^(-10)*1*x(5)^(4) + 0.55*x(3) + 1.34*x(1) - 2401.87*x(2) + 2400*Tg2;
F(3) = 0.124*G - 4.88*10^(-8)*x(3)^(4) + 2.44*10^(-8)*1*x(2)^(4) + 2.44*10^(-8)*1*x(5)^(4)- 50.938*x(3) + 11.502*x(6) + 1.836* x(2) + 37.60*Ta;
F(4) = 0.011*G - 8.70*10^(-8)*x(5)^(4) + 4.35*10^(-10)*x(3)^(4)+ 4.35*10^(-10)*x(2)^(4) + 0.83*x(6) + 0.112*x(3) + 0.112*x(2) - (1.055 + (112.7/1))*x(5) + (112.7/1)*Tf;
F(5) = 2.17*10^(-3)*G - 1.6*10^(-10)*x(4)^(4) + 8.01*10^(-11)*x(7)^(4) + 8.01*10^(-11)*x(2)^(4) - 69.07*x(4) + 3.77*10^(-4)*x(7) + 0.02*x(3) + 0.02*x(2) + 69*Tl;
F(6) = -52.068*x(6) + 0.412*x(3) + 0.368*x(4)+ 0.368*x(5) + 0.46*x(2) + 50.78*Tb; 
F(7)= 3.77*10^(-4)*x(4) + 8.01*10^(-11)*x(4)^(4) + 0.092*x(5) - 1254.1*x(7) - 8.01*10^(-11)*x(7)^(4) + 1254*Th;
end

[Geoff Hayes]

Bindhu - what is your question? Is there an error with the above or is something else wrong? Please clarify.

[John D'Errico]

I have a question: is there any meaning in the result if a solution is found? Why do I say that?

I ask my leading question because there won't be any meaning that can be attributed. That because the coefficients in this complex mess of equations are only significant to 3 decimal places. Yet the unknowns are apparently on the order of 300. What is done with them? Those unknowns are raised to powers that are as large as the 4th power.

What is 300^4?

300^4
ans =
                8100000000

Yet now combinations of these powers and coefficients that are given only to 3 significant digits will result in something mathematically meaningless, yet a great deal of effort will be made to extract a result, and probably great significance attributed to that result.

A wonderful thing are computers. They allow you to do all sorts of things that will result in virtually random results.

And, yes, these comments are absolutely serious. By trying to solve a problem with numbers as large as you are doing, yet using only 3 significant digits, this will result in computational garbage.

Answer 1

[Alex Sha]

refer the results below:

Constant G	x2	x1	x4	x3	x5	x6	x7
600	301.524350251906	299.992603098721	301.890052790606	305.92202132398	296.246654676285	303.841426255074	299.997914862015
700	301.525505891803	299.994372553396	301.893257963871	306.142245703105	296.255916331741	303.843267152199	299.997915564933
800	301.526662017238	299.99614200865	301.896463123691	306.362423019274	296.26517805246	303.845107681584	299.997916267857
900	301.527818628596	299.997911464483	301.899668270053	306.582553234965	296.274439838541	303.846947842935	299.997916970786
1000	301.528975726264	299.999680920896	301.902873402948	306.802636312723	296.28370169008	303.84878763596	299.99791767372
1100	301.530133310628	300.001450377889	301.906078522364	307.022672215155	296.292963607175	303.850627060367	299.99791837666
1200	301.531291382071	300.003219835462	301.909283628292	307.242660904934	296.302225589924	303.852466115866	299.997919079605

[Bindhu PR]

HOW CAN I GET THESE ANSWERS

CAN YOU PLEASE EXPLAIN

[Alex Sha]

Hi, Bindhu, I used one package other than Matlab, much easy, with global solutions, the code looks like below:

LoopConstant G=[600:100:1200];
Constant Tg1 = 300, Tg2 = 301.5, Ta = 305.8, Tl = 302, Tf = 302, Tb = 302, Th = 300;
Function
0.0425*g + 1.41*10^(-8)*x2^(4) + 1.34*x2 - 9.12*10^(-9)*x1^(4) + 341 - 2402.77*x1 + 2400*tg1;
0.0204*g - (3.48*10^(-8) + 4.35*10^(-10)*1)*x2^(4) + 1.41*10^(-8)*x1^(4) + 8.01*10^(-11)* x4^(4) + 2.43*10^(-8)*x3^(4) + 4.35*10^(-10)*1*x5^(4) + 0.55*x3 + 1.34*x1 - 2401.87*x2 + 2400*tg2;
0.124*g - 4.88*10^(-8)*x3^(4) + 2.44*10^(-8)*1*x2^(4) + 2.44*10^(-8)*1*x5^(4)- 50.938*x3 + 11.502*x6 + 1.836* x2 + 37.60*ta;
0.011*g - 8.70*10^(-8)*x5^(4) + 4.35*10^(-10)*x3^(4)+ 4.35*10^(-10)*x2^(4) + 0.83*x6 + 0.112*x3 + 0.112*x2 - (1.055 + (112.7/1))*x5 + (112.7/1)*tf;
2.17*10^(-3)*g - 1.6*10^(-10)*x4^(4) + 8.01*10^(-11)*x7^(4) + 8.01*10^(-11)*x2^(4) - 69.07*x4 + 3.77*10^(-4)*x7 + 0.02*x3 + 0.02*x2 + 69*tl;
-52.068*x6 + 0.412*x3 + 0.368*x4+ 0.368*x5 + 0.46*x2 + 50.78*tb;
3.77*10^(-4)*x4 + 8.01*10^(-11)*x4^(4) + 0.092*x5 - 1254.1*x7 - 8.01*10^(-11)*x7^(4) + 1254*th;

[Bindhu PR]

where can i run these codes for getting the answers can you please explain

[Bindhu PR]

which is the pack for running these codes

[Bindhu PR]

why in these codes small g is used instead of G.Actually different Values for G are needed from 600 to 1200

[Alex Sha]

Hi, it is a package called "1stOpt", in this package, it is not case-sensitive, so "g" and "G" mean same one

[Bindhu PR]

is it possible to do in matlab.any modification to be done in the above code to run in matlab

[Bindhu PR]

i want to run the code in matlab i presented almost my project in matlab

[Alex Sha]

should be difficult since the algorithms used in Matlab, for example fsolve, is local optimization algorithm, not global optimization algorithms, so the results from Matlab heavily depends on the guess of initial start values, although there is GA toolbox with the global optimization ability, but actually, the effect of GA is far to say good.

[Bindhu PR]

thank you

[Bindhu PR]

sir the answer are not correct here while variying the values of G from 600 to 1200 there is no variations in the answers.

[Alex Sha]

Which version of 1stOpt you used? The latest version is 8.0