I just plotted this graph 
My question is which grid gives the best accuracy for $d = R/2$? I mean how do I explain in what ways it is more accurate.
This is my explanation.
Grid 2 gives a better accuracy than Grid 1 because it is more closer to the actual solution so it must be more accurate. Even though, Grid 1 and 2 give accurate result.
Any suggestions will be appreciated. Thanks in advance!
Computer generated graphs are notoriously unreliable and can easily deceive you. In particular, you current graph hides details near $0$. You have presented no evidence to support the assumption that the observed behavior near $x = \pm 3$ continues towards $0$. Until you compute the relative error and focus on a small neighbourhood of $0$ you will remain in the dark as to which approximation is the best. If $x \to T(x)$ is your target function and $x \to A(x)$ is an approximation, then you should plot $$x \to R(x)=\frac{T(x)-A(x)}{T(x)}.$$
The graphics suggest that you are using MATLAB, so remember the period '.' which ensures the division needed for the computation of $R$ is done componentwise.