Non zero errors obtained when zero error is expected

The below shown graph represents errors (between an exact solution and an approxmimate solution) for different number of nodes (ranging from 5 to 100). The error values are expected to be zero (as exact and apprximate solutions are equal) but a considerably smaller value is obtained which is closer to machine precision (eps) but not equal to it.

The same graph is generated from a different machine which is installed with matlab R2020a. It also didn't give zero error but a considerably smaller value is obtained which is closer to machine precision (eps) but not equal to it and was different from ones generated with first machine. (Both machines uses windows 10 as operating system).

1. What could be the possible reason for non zero errors?
2. Why are different machines giving different values of errors?

Thanks in advance,

Sree Raj V

[dpb]

W/o what the code is it is impossible to comment other than in general but

1. Clearly the approximate and exact solutions aren't actually identical. That's not surprising; otherwise they would both be "exact solutions",
2. That both machines use Win10 doesn't prevent them from using different processors and while you say one used R2020a, you didn't say which MATLAB release the other used. It's possible there could be an internals difference there; Mathworks routinely makes upgrades/enhancements between releases or even in patches between releases. It's also possible there may be some initial conditions between how the code is run that is different between the two cases; we have no way to know any such details.

[Walter Roberson]

If one has an AMD CPU then it will calculate differently than an Intel CPU.

[Sree Raj V]

@dpb The code is attached herewith for reference.

Matlab versions are: 1. R2020a

2. R2020b

@Walter Roberson Both used intel CPUs, i7 and i5 for R2020a & R2020b respectively