Solving numerical integral

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Hello,

I would like to ask someone's help to get more accurate solution for an integral.

I have a data set which should be integrated with the given integral (see picture).

So far, I solved this problem like this:
1. Precalculated the derivative
2. than use a simple rectangular integration to compute the integral

The problem is the results contains some negative error because the first point is not considered.
(between t=z and t1)

I did not found any way to use the Igor built in integrals for this problem (I'm new around).

I would like to ask some advice how to move forward.

Thanks a lot!
You should take a look at Integrate1D, which will do a numerical approximation of an analytic integration. You provide an Igor user-defined function that evaluates the integrand. You will need some expression for Omega(t) and d(omega)/dt, or at least an approximation of them.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

April 28, 2011 at 04:52 pm - Permalink

johnweeks wrote:
You should take a look at Integrate1D, which will do a numerical approximation of an analytic integration. You provide an Igor user-defined function that evaluates the integrand. You will need some expression for Omega(t) and d(omega)/dt, or at least an approximation of them.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com


Yes, I tried to use it but I run in to problems. The omega(t) (measured data at each Z point) is a function of Z of corse. For the hole data set it is difficult
the approximate but what I found is that I can fit with a small proximity of the data with a polynomial function than the expressions for both are easy and I can call the integrate1D.... move the proximity .... finally sum it up. (Of corse this will take kind of long). But no better way at this moment

April 29, 2011 at 01:07 am - Permalink