Is there a function in Matlab that is similar to "cumtrapz" but uses a more accurate method of array integration (such as Simpson's rule)?

Is there a function in Matlab that is similar to "cumtrapz" but uses a more accurate method of array integration (such as Simpson's rule)? (i.e., to integrate a nonanalytic function (represented by an array))

Answer 1

[John D'Errico]

You COULD use a spline interpolant, then integrating the spline. That would be a higher order integration. (Pchip MAY be a better choice than spline, although spline will be theoretically a higher order as an integration tool here.)

Or you could use a Simpsons rule. Note that it is easy to think you are doing a better job, because the integration rule is of a "higher" polynomial order. In fact, it is trivial to give you a set of points that will cause a simple high order integration to fail miserably.

[Neil Gelman]

Thank you very much for your suggestion and explanation. I will try the spline.

[John D'Errico]

Note that integrating a spline function can be done analytically, since they are polynomial segments. (Again, pchip is also essentially a spline, but possibly a better choice for many problem.)