Does the workstation effects the output accuracy?
 

Recently I just developed a code using Matlab. The results need about 6000 time steps to converged. But the example shows that it should be able to converge at about 1200 time steps. So I checked the results for every calculation, and there is a problem. For grid point 16 or 17, the results for every calculation agreed very well. But there are some variation at grid point 15, and this small variation caused my algorithm take more time to converge. My lecturer told me that it maybe 2 reaons: 1)Round-off errors. 2)Caused by the machine itself.

What I know is that the workstation only affect the speed of computing. Will it affect the accuracy of the output as well? This really puzzled me. If this is not the reason, then is it because of my boundary condition?