The context of the question:
I had plotted a certain 2D function in hydrodynamics by plotting a set of 25 points. Then, I tried to discretize the underlying equations of hydrodynamics to obtain the discrete limit of the same function (i.e. using moving particles and their interactions) and found that both the functions nearly overlaps each other as expected.
But I noticed an unusual thing when I calculated the fractional deviation of the discretized function from the actual hydrodynamic function. Though the fractional deviation was negligible, it followed no distinct pattern and was fluctuating.
The question:
In error analysis, should errors also need to have any particular pattern? If the errors are random as in the above context, is there something wrong in my calculations?
There are lots of different types and sources of error; some look random, some do not. For example, truncation error (e.g. replacing a convergent infinite series by the sum of a finite number of terms) tends to have a pattern: when convergence is rapid, the error may be dominated by the first omitted term. On the other hand, roundoff error tends to look random.