A novel optimized computational approach to investigate the motion of a single-walled carbon nanotube conveying fluid flow

In the current investigation, the nonlinear vibration of a single-walled carbon nanotube is analyzed both numerically and analytically. The nonlocal beam model and Pasternak foundation are employed to evaluate the nanotube's vibration behavior. The deflection equation, which serves as the primary variable in this study, effectively captures the nonlinear vibrational characteristics commonly observed in engineering applications. A novel meshless scheme—the optimized Akbari-Ganji method (OAGM)—has been developed and applied to solve the governing differential equation. The term optimization has been intentionally emphasized in this context to highlight a key innovation of the study: the refinement and enhancement of the original Akbari-Ganji method through systematic optimization techniques to improve convergence, accuracy, and computational efficiency. This advancement not only distinguishes the present research from prior approaches but also underscores its practical applicability in complex engineering problems. The validity of the proposed method is demonstrated through comparison with previous studies, revealing that the OAGM delivers a fast, reliable, and highly accurate analytical approximation.