Boling point problem with bisection method

Hi everybody! im trying to solve a boiling problem with bisection method. but there is something wrong.

Question is:

To solve it, i wrote these codes: but there is an error (too many input arguments)

function bisection(a, b, eps)
iter=0; 
  global k A B C
 k=[0.05 0.15 0.5 0.3];
 A=[15.8333 15.8366 15.8737 15.9426];
 B=[2477.07 2697.55 2911.32 3120.29];
 C=[-39.94 -48.78 -56.51 -63.63]; 
 
    xm = (a+b)/2;
    x=[a b xm];
    f = fonk(x);
 for i=1:4
     exp(A-B/(x+C))*k*133.32-1e5;
 end
  
while abs(a-b)>eps 

    if f(1)*f(3) <=0 
        b = xm;
        elseif f(2)*f(3)<=0 
        a = xm;
       else
       disp('You have a ill conditioned function or multiple root'); 
    end
    iter=iter+1;
end
fprintf('Bulunan kök değeri (sürtünme katsayısı) = %8.5f \n', (a+b)/2);
fprintf('%i. iterasyonda sonuca ulaşıldı. \n', iter); 
end

function [f] = fonk(x)
global k A B C
   f=exp(A-B/(x+C))*k*133.32-1e5;
end 

[darova]

Why are using x here instead of T?

function [f] = fonk(x)
global k A B C
   f=exp(A-B/(x+C))*k*133.32-1e5;
end 

I don't see you defined T somewhere

[Arctgx]

I think it doesn't matter using x or T variable. The problem is not x or T. The error is (too many input arguments) in Matlab.

[darova]

I don't understand which value you are trying to find

[Ameer Hamza]

Which line gives this error? What are the values of a, b, and eps when you call this function? vector A, B, and C are 1x4, but x is 1x3 so this expression

exp(A-B/(x+C))*k*133.32-1e5;

will also give error.

[Arctgx]

darova, i used "k" for x. and i used "x" for T. i want to find mixture's boiling point.

Ameer, what is the solution?

Answer 1

[Ameer Hamza]

Try this code. Check the differences with your code to see the mistakes

x = bisection(300, 400, 0.001);

function xm = bisection(a, b, eps)
    iter = 0;
    global k A B C
    k=[0.05 0.15 0.5 0.3];
    A=[15.8333 15.8366 15.8737 15.9426];
    B=[2477.07 2697.55 2911.32 3120.29];
    C=[-39.94 -48.78 -56.51 -63.63];

    while abs(a-b)>eps
        xm = (a+b)/2;
        
        if fonk(a)*fonk(xm) <=0
            b = xm;
        elseif fonk(xm)*fonk(b)<=0
            a = xm;
        else
            disp('You have a ill conditioned function or multiple root');
        end
        iter=iter+1;
    end
    fprintf('Bulunan kök değeri (sürtünme katsayısı) = %8.5f \n', (a+b)/2);
    fprintf('%i. iterasyonda sonuca ulaşıldı. \n', iter);
end

function [f] = fonk(x)
    global k A B C
    f=sum(exp(A-B./(x+C)).*k*133.32)-1e5;
end

[Arctgx]

Thank you so much Ameer! Now i saw the mistakes.

1) First mistake, scaler and vector multiplication.

2) Second mistake, about fonk(x)

3) Third mistake, forgetting to use sum function

[Ameer Hamza]

Correct. I am glad that my code is helpful.

[GeotechnicalEngr]

Hi,i have a question. When we define 'while' part and use the code that Arctgx shared,

while abs(a-b)>eps 
    if f(1)*f(3) <=0 
        b = xm;
        elseif f(2)*f(3)<=0 
        a = xm;
       else

what can i do for not to get the 'Matrix dimensions must agree' error?

[Ameer Hamza]

How is the function f defined?

[GeotechnicalEngr]

function bisection(a, b, eps)
iter=0;
a=330;
b=398.75;
eps=1e-5;
 
iter=0;
global k A B C 
k=[0.05 0.15 0.50 0.30];
A=[15.8333 15.8366 15.8737 15.9426];
B=[2477.07 2697.55 2911.32 3120.29];
C=[-39.94 -48.78 -56.51 -63.63];
 
while abs(a-b)>eps
    xm = (a+b)/2;
      x=[a b xm];
      f = fonk(x);
    if f(1)*f(3) <=0
        b = xm;
        elseif f(2)*f(3)<=0
        a = xm;
       else

       disp('You have a ill conditioned function or multiple root'); 
    end
        iter=iter+1;
 
end
fprintf('Root value) = %8.5f \n', (a+b)/2);
end
 
 
function [f] = fonk(x)
global k A B C
f=sum(exp(A-B./(x+C)).*k*133.32)-1e5;
end 
 

I wrote these code and get Matrix dimensions must agree error.

[Ameer Hamza]

GeotechnicalEngr, you are using Arctgx code. Check the code in my answer to see how to correct this issue.

[GeotechnicalEngr]

Thanks for your answer. But i know that i am using Arctgx code. What my teacher want is not to do any changes when coding bisection method part. That's why i am trying to solve the problem this way, perhaps he has overlooked something.

By the way i tried your code and it works. Thanks.

[Ameer Hamza]

try this

x = bisection(300, 400, 0.001);

function xm = bisection(a, b, eps)
iter=0;
a=330;
b=398.75;
eps=1e-5;

iter=0;
global k A B C
k=[0.05 0.15 0.50 0.30];
A=[15.8333 15.8366 15.8737 15.9426];
B=[2477.07 2697.55 2911.32 3120.29];
C=[-39.94 -48.78 -56.51 -63.63];

while abs(a-b)>eps
    xm = (a+b)/2;
    x=[a b xm];
    f(1) = fonk(x(1));
    f(2) = fonk(x(2));
    f(3) = fonk(x(3));
    if f(1)*f(3) <=0
        b = xm;
    elseif f(2)*f(3)<=0
        a = xm;
    else
        disp('You have a ill conditioned function or multiple root');
    end
    iter=iter+1;
end
fprintf('Root value) = %8.5f \n', (a+b)/2);
end


function [f] = fonk(x)
global k A B C
f=sum(exp(A-B./(x+C)).*k*133.32)-1e5;
end

[GeotechnicalEngr]

Code is working now. Thank you so much for your help!