Comparing numerical results with different integration grids sizes (MATLAB)

I am trying to compare the numerical results of a complex integral using Matlab's integral.

In particular, I want to examine the accuracy of the results using

a fixed integration interval [0,T],
but different sparseness or integration grid sizes.

Is there a way to specify integration grid sizes (i.e.: number of equally spaced grid points) when using Matlab's integral? Or should I find other alternatives?

Solution

Is there a way to specify integration grid sizes (i.e.: number of equally spaced grid points) when using MATLAB's integral?

Short answer: No.

The documentation says you can enter only:

q = integral(fun,xmin,xmax,Name,Value) specifies additional options with one or more Name,Value pair arguments. For example, specify 'WayPoints' followed by a vector of real or complex numbers to indicate specific points for the integrator to use.

So, we scroll down a bit and read which name/value pairs are allowed and find:

'AbsTol', absolute error tolerance
'RelTol', relative error tolerance
'ArrayValued', array-valued function flag
'Waypoints', integration waypoints

MATLAB automatically optimises the integral and computes in numerically (of course), which ends for a given error, defined by 'AbsTol' and 'RelTol'. I'd just go with that.

If you do want to specify integration step size you can check what happens if you specify 'Waypoints' to be [0:1/(100*T):T]. I'd go with integrating it myself though, using a simple Riemann sum implementation.