Solving 18 equations in iteration until 3 variables within a percent

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RANJITH REDDY KALLURI 2020-9-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/595093-solving-18-equations-in-iteration-until-3-variables-within-a-percent

评论： J. Alex Lee 2020-9-18

Example: following are the equations needed to be solved for convergence of A & B within 1% ; Initial assumption of A is 0.8, B is 0.375.

Eq 1: A = B/(1-C);

Eq 2: B = (D + E)/(F +G);

Eq 3: C = D*E + F*B;

Eq 4: D = 2*A/B; etc.

I could technically write my code using while loop as below, but the equations i have are actually complex and cannot be solved as i did.

I'm trying to find if there is a better way of doing such iterations with few or little known values and guesses.

P.S. The equations and values in here are just to demonstrate, it might or might not actually converge.

%known values
e = 10; f = 5; g = 1.75
% initial guess
a = 0.8;
b = 0.75;
% Temp variables
a_temp = a;
b_temp = b;
a_conv = 0;
b_conv = 0;
while i = 1:100 % to prevent from staying in loop forever
    d = 2*a/b; % eq 4
    b = (d + e)/(f + g); %eq 2
    c = (d*e) + (f*g); % eq 3
    a = b/(1-c); % eq 1
    a_conv = ( a - a_conv)/a;
    b_conv  = (b - b_conv)/b;
    
    if a_conv <0.01 && b_conv<0.01
        break
    else
        a_conv = a;
        b_conv = b;
    end
end

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RANJITH REDDY KALLURI 2020-9-18

There are no differential equations or functions, so I am not sure if they can be called Picard iterations. Can you help me understand on how to use fsolve ? Thank you

J. Alex Lee 2020-9-18

在 MATLAB Online 中打开

have you read the docs for fsolve? you first need to set up the equations in residual form, i.e.,

r(1) = A - B/(1-C)
r(2) = B - (D + E)/(F +G);
r(3) = C - (D*E + F*B);
r(4) = D - 2*A/B;

etc.

Then you have a standard root finding problem, just plug into fsolve...

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Mathematics and Optimization Optimization Toolbox Optimization Results Solver Outputs and Iterative Display

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