Nonlinear solutions with 7 variables my initial Guess is not working in the program

syms G;
G = 600:100:1200;
disp(G)
x0 = [310 310 310 311 309 300 300];%initial guess
options = optimoptions('fsolve','Display','off');
X = zeros(1,length(G)); % use X, instead of X(i), initialize with zeros
for i = 1:length(G) % start the loop counter from 1
fsol = fsolve(@(x) solutionsproblem(x,G(i)),x0,options);
X(i,:) = fsol; end
Tg1 = x(:,1); Tg2 = x(:,2); Ta = x(:,3); Tl = x(:,4); Tf = x(:,5); Tb = x(:,6); Th = x(:,7);
disp(X);

 function F = solutionsproblem(x,G)

 syms N;
syms A;
%assign values to constants
N = 15;
A = 1;
Tg1 = 300;
Tg2 = 301.5;
Ta = 305.8;
Tl = 302;
Tf = 302;
Tb = 302;
Th = 300;
F(1) = 0.0425*G + 1.417*10^(-8)*x(2)^(4) + 0.95*x(2) - 1.967*10^(-8)*x(1)^(4) + 1098.572 - 2404.5*x(1) + 2400*Tg1;
F(2) = 0.0204*G + (-4.888*10^(-8) - 7.709*10^(-11)*N*A)*x(2)^(4) + 1.41*10^(-8)*x(1)^(4) + 4.54*10^(-10)* x(4)^(4) + 3.08*10^(-8)*x(3)^(4) + 7.709*10^(-11)*N*A*x(5)^(4) + 0.55*x(3) + 0.95*x(1) - 2401.5*x(2) - 2400*Tg2;
F(3) = 0.124*G - 6.098*10^(-8)*x(3)^(4) + 3.049*10^(-8)*x(2)^(4) + 3.049*10^(-8)*x(5)^(4)- 568.69*x(3) + 0.236*x(6) + 1.183* x(2) + 567.9*Ta;
F(4) = 4.06*10^(-3)*G - 90.37*10^(-10)*x(4)^(4) + 9.88*10^(-10)*x(7)^(4)+ 9.88*10^(-10)*x(2)^(4) + 0.08*x(7) + 0.044*x(3) + 0.044*x(2) - 132.687*x(4) + 132.44*Tl;
F(5) = 3.686*10^(-4)*N*A*G + 3.049*10^(-8)*x(3)^(4) + 7.7*10^(-11)*x(2)^(4) - 3.056*10^(-8)*x(5)^(4) + 3.88*10^(-4)*N*x(6) + 3.52*10^(-3)*N*A*(x(3) + x(2)) - (3.88*10^(-4)*N + 7.04*10^(-3)*N*A + 215)*x(5) - 215*Tf;
F(6) = 0.386*x(3) + 0.18362*x(7) + 3.88*10^(-4)*N*x(5) + 0.1*x(2) - (194.269 + 3.88*10^(-4)*N)*x(5) + 193.6*Tb;
F(7)= 0.08*x(4) + 9.88*10^(-10)*(x(4)^(4) - x(7)^(4)) + 0.0706*x(6) - 838.79*x(7) + 838.22*Th;
 end

Answer 1

[Ameer Hamza]

What do you mean by "not working"? The value of solutionsproblem at the points found by fsolve() is on the order of 1e-9. You can further tighten this tolerance value, but I guess this should be sufficient enough for most practical applications. Add the following for-loop at the end of your code and check the output in the command window

for i=1:length(G)
    y = solutionsproblem(X(i,:), G(i));
    disp(y)
end

Result

   1.0e-09 *
    0.1164    0.1164         0   -0.0073    0.0509    0.0073   -0.0291
   1.0e-09 *
    0.1164         0   -0.0582   -0.0073    0.0291         0    0.0873
   1.0e-09 *
   -0.1164   -0.1164    0.0291         0   -0.0437         0   -0.0291
   1.0e-09 *
    0.1164    0.1164    0.1455   -0.0073    0.0509    0.0073    0.0582
   1.0e-09 *
   -0.1164    0.1164    0.1455         0         0    0.0073   -0.0291
   1.0e-09 *
         0         0    0.1746   -0.0073   -0.0146         0    0.0291
   1.0e-09 *
   -0.1164   -0.1164    0.1164         0         0    0.0146    0.0291

[Adithya Valavi]

My problem is that the answer has to come above 300 and the initial Guess is not working

[Adithya Valavi]

x0 = [310 310 310 311 309 300 300]; So the value should be near by this value

[Ameer Hamza]

Not necessarily near x0. This is just an initial guess. Are you sure that a solution of the equations lies near x0? Also note that the variables 1,2,4, and 5 are near 300. Only 3 and 6 are far.

[Alex Sha]

I got the result below:

G	x1	x2	x3	x4	x5	x6	x7
600	299.764156633882	-254.604230258111	1378.42810435931	302.586579569078	304.130925344338	3517902.19848446	595.784285276060
700	299.765922601135	-254.603473577461	1378.42739326552	302.589583773355	304.130919856780	3517846.02039974	595.779562215228
800	299.767688568363	-254.602716896794	1378.42668217067	302.592587977665	304.130914369218	3517789.84231252	595.774839154086
900	299.769454535567	-254.601960216108	1378.42597107476	302.595592182008	304.130908881655	3517733.66422282	595.770116092635
1000	299.771220502746	-254.601203535404	1378.42525997780	302.598596386383	304.130903394089	3517677.48613064	595.765393030875
1100	299.772986469899	-254.600446854683	1378.42454887978	302.601600590791	304.130897906520	3517621.30803596	595.760669968806
1200	299.774752437028	-254.599690173943	1378.42383778070	302.604604795231	304.130892418949	3517565.12993881	595.755946906428

[Adithya Valavi]

What changes did you make to get this output

[Ameer Hamza]

I guess Alex used 1stOpt. That is not a Mathworks product. fsolve() also gives the same solution. It is just printed differently by default. For example, you can display MATLAB solution like this too

for i=1:length(G)
    fprintf([repmat('%12f\t', 1, 7) '\n'], X(i,:));
end

Result

  299.764157	 -254.604230	 1378.428104	  302.586580	  304.130925	3517902.198484	  595.784285	
  299.765923	 -254.603474	 1378.427393	  302.589584	  304.130920	3517846.020400	  595.779562	
  299.767689	 -254.602717	 1378.426682	  302.592588	  304.130914	3517789.842313	  595.774839	
  299.769455	 -254.601960	 1378.425971	  302.595592	  304.130909	3517733.664223	  595.770116	
  299.771221	 -254.601204	 1378.425260	  302.598596	  304.130903	3517677.486131	  595.765393	
  299.772986	 -254.600447	 1378.424549	  302.601601	  304.130898	3517621.308036	  595.760670	
  299.774752	 -254.599690	 1378.423838	  302.604605	  304.130892	3517565.129939	  595.755947