Matlab keeps being "busy" when computing the integral of a function

Hello guys,

I'm having a problem running a very simple code and I cannot figure out why.

The code is to find the definite integral of a function whose coefficients are variant. One limit of the integral is also variant.

I have quite a few computations to make but I started with the first two.

syms g z
[a,b] = meshgrid(1.2:.02:1.36,0.54:.02:0.6);

k = ((a./b)+((a./b).^2-4).^(1/2))./(2*a);

for i = 1:1
    for j = 1:2
        g =(a(i,j)*z)^2/(1+(a(i,j)*z)^2)-b(i,j)*z;
        c(i,j) = int(g, z, 0, k(i,j));
    end
end

For i=1, j=1, the code works fine but for i=1, j=2, it takes like forever for Matlab to compute. I have to use ctrl+c to stop it.

I don't see any singular behaviours of the function in the interval of integration.

I'm using Matlab R2014a. Maybe there are some stupid errors in the code but for the moment I cannot see it.

Could anyone find the problem?

Thank you!

Answer 1

[madhan ravi]

Just convert symbolic integral (int()) to numerical integral (integral()) using matlabFunction() because the symbolic integrator is finding it difficult to solve.

syms z
[a,b] = meshgrid(1.2:.02:1.36,0.54:.02:0.6);
k = ((a./b)+((a./b).^2-4).^(1/2))./(2*a);
c=zeros(size(k));  % preallocate
for i = 1:size(k,1)  % I believe you want to calculate the integral for entire k 
    for j = 1:size(k,2)
        g =matlabFunction((a(i,j)*z)^2/(1+(a(i,j)*z)^2)-b(i,j)*z);
        c(i,j) = integral(g, 0, k(i,j));
    end
end

Gives:

>> c

c =

  Columns 1 through 7

    0.0098    0.0177    0.0255    0.0334    0.0413    0.0492    0.0571
   -0.0064    0.0007    0.0079    0.0151    0.0225    0.0298    0.0371
   -0.0196   -0.0135   -0.0071   -0.0005    0.0062    0.0129    0.0197
   -0.0295   -0.0247   -0.0193   -0.0136   -0.0077   -0.0016    0.0047

  Columns 8 through 9

    0.0649    0.0727
    0.0445    0.0518
    0.0266    0.0334
    0.0110    0.0173

>> 

[Zhengyang Zhang]

Thank you very much! This helped!

[madhan ravi]

Anytime :)

[Hernan Larriva]

OHHHH...thanks a lot , I had the same problem..I solved with your answer.......Regards from Barcelona-Spain