Numerical integration and errors

[PorridgeMan]

Hi,

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.

 

[fresh_42]

Here is a short paper with some general rules for the error analysis of numerical integration:
http://pages.cs.wisc.edu/~amos/412/lecture-notes/lecture19.pdf

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.

Maybe you could attach $\varepsilon_i$ to your input variables and see whether they add up, or better, are divided by at some place of the algorithm you use.