*Onvergence of HAM*

The HAM scheme has the auxiliary constants <sup>ђ</sup> *<sup>f</sup>* and <sup>ђ</sup><sup>Θ</sup> that constantly control and modify the solution convergence. For an appropriate value of <sup>ђ</sup> *<sup>f</sup>* and <sup>ђ</sup>Θ, we perform 18th order approximation. The appropriate region <sup>ђ</sup> *<sup>f</sup>* and <sup>ђ</sup><sup>Θ</sup> for SWCNTs lies between −0.1 ≤ <sup>ђ</sup> *<sup>f</sup>* ≤ −0.5 and − 0.2 ≤ <sup>ђ</sup><sup>Θ</sup> ≤ 1.9, while for MWCNTs, the suitable region is between −0.2 ≤ <sup>ђ</sup> *<sup>f</sup>* ≤ −0.8 and − 0.1 ≤ <sup>ђ</sup><sup>Θ</sup> ≤ 1.5.
