Coupled NT and Decomposition technique (NTADM), is a powerful methodology for dealing with PDEs. The technique used NT to eliminate the time of the driving equation, whereas ADM tackles nonlinear variables methodically without resorting to linearization or numerical discretization. This work employs NTADM to solve a fourth-order NPDE and obtains approximate solutions up to the fifth iteration. The features of the solutions emerging from this show effortless, steady behavior in both space and time. The numerical results show that accuracy improves as the approximation order increases. The absolute error also remains below 1 across most of the computational domain, indicating very strong convergence. These results show that NTADM is a strong and reliable technique for analyzing complex high-order nonlinear PDE models.