function handle producing different output

Hi,

I am trying to write a code to find the intersection of the two curve:

A = @(m) -2.*(1/1.895.*((1+(1.4-1).*m.^2/2).^(1.4/(1.4-1)))-1)./(1.4.*m.^2);
B = @(m) (0.38./sqrt(1-m.^2));

m_lower = 0;
m_upper = 1;
m_mid = (m_lower+m_upper)/2;

{while abs(A(m_mid))-(B(m_mid))) > 0

      if (A(m_mid))<(B(m_mid))
          m_lower = m_mid
      else 
          m_upper = m_mid
      end
      m_mid = (m_lower+m_upper)/2

end

However, when I tried to plot the curves, (i.e. fplot(A,[0 1]);) it gives me an incorrect curve. but when I tried to solve individually A(1) etc. etc., it produce the correct answer. Similarly when I tried to loop the equation in the while loop, it just goes to infinity because it using the wrong curve.

Many thanks in advance!

[www]

What do I have to do if I want to continue the loop is A(m_mid) ~= B(m_mid)? Is there another function or neater way?

Pardon me, I am very new to MATLAB!

Answer 1

[Star Strider]

Your functions produce complex results, so the best you can hope for is to compare the absolute values of them:

A = @(m) -2.*(1/1.895.*((1+(1.4-1).*m.^2/2).^(1.4/(1.4-1)))-1)./(1.4.*m.^2);
B = @(m) (0.38./sqrt(1-m.^2));

AminusB = @(m) abs(A(m)) - abs(B(m));

IntSct(1) = fzero(AminusB, 0.5)
IntSct(2) = fzero(AminusB, 1.5)

x = linspace(0, 5, 100);

figure(1)
semilogy(x, abs(A(x)),  x, abs(B(x)) )
hold on
plot(IntSct(1), abs(A(IntSct(1))), 'gp', 'MarkerSize',10)
plot(IntSct(2), abs(A(IntSct(2))), 'gp', 'MarkerSize',10)
hold off
grid

Producing:

IntSct =
   754.2877e-003     1.3359e+000

I found the intersections by taking the differences between the absolute values of your functions, and then letting the fzero function find the zero crossings.

[www]

is there a way to use while loop to execute a bisection method to produce a table of iterations?

[Star Strider]

This is how I would do it:

A = @(m) -2.*(1/1.895.*((1+(1.4-1).*m.^2/2).^(1.4/(1.4-1)))-1)./(1.4.*m.^2);
B = @(m) (0.38./sqrt(1-m.^2));

AminusB = @(m) abs(A(m)) - abs(B(m));

dw = 1E-4;
w = dw;
Val = AminusB(w);
while Val > 0
    Val = AminusB(w);
    w = w + dw;
end
fprintf('\nA = B at %.4f with value = %.4f\n', w, Val)

A = B at 0.7544 with value = -0.0001

[www]

You have saved this poor student! T.T

[Star Strider]

As always, my pleasure!

[www]

I was wondering how do I alter the code above to use the bisection method where I converge the intersection of A and B from a upper and lower limit and achieve a tabled results similar to : @8.54mins https://www.youtube.com/watch?v=ZJAPBTRI3Yk @8.54mins

My case would be to match A=B.

[Star Strider]

The bisection method is a root-finding method, so I would use it with my derived ‘AminusB’ to find the root. That will be where A=B.

Answer 2

[jgg]

Not sure what the deal is, but this works:

 A_vals = A(0.1:0.01:1);
 vals = 0.1:0.01:1;
 B_vals = B(0.1:0.01:1);
 plot(vals,A_vals);
 hold on
 plot(vals,B_vals);

You can see it works here too:

 fplot(B,[0.1,0.99])
 hold on
 fplot(A,[0.1,0.99])

I think the asymptotes are causing it to look funny; I'm not convinced it's wrong though.