Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I was wondering if anyone can point me to a general treatment of errors when doing numerical integration of measured variables?

My problem is that I am integrating force with respect to displacement (of a piston) in an attempt to calculate work...and getting some impossible numbers. The force and displacement values are sampled from analogue transducers in a laboratory set-up. The data acquisition system samples each signal sequentially and creates trends with their own unique time bases. The frequency of sampling varies somewhat and I have no control over this. Anyway, to do the integration I then need to interpolate the acquired values at common points in time (e.g. every 0.1 s). I therefore have multiple sources of error - the initial measurement (instrument calibration), the sampling, the quantisation and finally the interpolation. I'm ignoring rounding and truncation in software for the time being.

I suspect these errors are adding up with adverse consequences, but I can't figure out how to derive an expression incorporating all the variables to assess their impact. This must be a common problem, but my old uni textbooks and Google haven't been much help. Any advice is much appreciated,

PorridgeMan.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Numerical integration and errors

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**