Integral: "Warning: Minimum step size reached"

Hi,

I'm trying to calculate an Integral the following:

xmin=c0/b;
xmax=zn+c0/b;

tw=@(w)(1./(b.*w.*sqrt(1-power(a,2).*power(b,2).*power(w,2))));
r=@(w)(a.*b.*w)./sqrt(1-power(a,2).*power(b,2).*power(w,2));
rx=integral(r,xmin,xmax)
t=integral(tw,xmin,xmax)

For

a=0.00067024
b=-0.06
c0=1480
cn=1492
z0=1000
zn=799.9523

it is working fine, however, for

a=0.00067024
b=0.0133
c0=1480
cn=1492
z0=1000
zn=1902.3

it gives me the following error:

Warning: Minimum step size reached near x = 112181. There may be a singularity, or the
tolerances may be too tight for this problem.

What am I doing wrong?

Answer 1

[Star Strider]

It is a warning, not an error. It is telling you that the integral function has encountered s singularity and cannot continue.

I would plot the function that is throwing that error to see what the function is doing at that value of the independent variable. You might want to integrate it piecewise below and above the region of that independent variable value.

Answer 2

[Anke Kügler]

Well, it is giving me results, but I don't know how to read them:

r=1.4201e+04 - 1.5011e+04i
t=9.5693 -10.0014i

what does the "i" mean? I've never seen that before (only for imaginary parts, but my results shouldn't be complex....)

[Star Strider]

The ‘i’ means you do have a complex value for the integration. It probably means you are taking the sqrt of a negative value.

Answer 3

[Walter Roberson]

In your formula r, if power(a,2)*power(b,2)*power(w,2) is greater than 1 then 1 minus that expression is negative and you would be taking sqrt() of a negative number.

power(a,2)*power(b,2) is fixed for any one run, so you can calculate the necessary w as

1/sqrt(power(a,2)*power(b,2))

or more simply 1/(a*b) . And if that is in the range xmin to xmax then your integral involves complex numbers.