  We investigate the quasinormal modes (QNMs) of the scalar field coupled to
the Einstein's tensor in the non-commutative geometry inspired black hole
spacetime. It is found that the lapse function of the non-commutative black
hole metric can be represented by a Kummer's confluent hypergeometric function,
which can effectively solve the problem that the numerical results of the QNMs
are sensitive to the model parameters and make the QNMs values more reliable.
We make a careful analysis of the scalar QNM frequencies by using several
numerical methods, and find that the numerical results obtained by the new WKB
method (the Pad\'e approximants) and the Mashhoon method
(P$\ddot{\text{o}}$schl-Teller potential method) are quite different from those
obtained by the asymptotic iterative method (AIM) and time-domain integration
method when the non-commutative parameter $\theta$ and coupling parameter
$\eta$ are large. The most obvious difference is that the numerical results
obtained by the AIM and the time-domain integration method appear a critical
value $\eta_c$ with an increase of $\eta$, which leads to the dynamical
instability. After carefully analyzing the numeral results, we conclude that
the numerical results obtained by the AIM and the time-domain integration
method are closer to the theoretical values than those obtained by the WKB
method and the Mashhoon method, when the $\theta$ and $\eta$ are large.
Moreover, through a numerical fitting, we obtain that the functional
relationship between the threshold $\eta_c$ and the non-commutative parameter
$\theta$ satisfies $\eta_{c}=a\theta^{b}+c$ for a fixed $l$ approximately. We
find that the stability of dynamics can be ensured in the $\eta<\eta_c(\theta,
l)$ region.
