The short-time evolution of a two-dimensional curvature-driven flow is investigated using smooth initial data. The governing equation is formulated for a height function f(x‚y‚t) over a rectangular domain and is evolved under its associated curvature operator. Two truncated Adomian Decomposition Method approximations, namely the first- and second-order schemes (ADM1 and ADM2), are derived and compared with a finite difference (FD) reference solution. To assess the accuracy and short-time behavior of the proposed methods, a smooth Gaussian initial condition is considered. The numerical results show that both ADM1 and ADM2 accurately capture the curvature-driven dynamics and agree closely with the FD solution within the short-time regime. The corresponding error distributions remain small and smooth over the computational domain, indicating stable and reliable performance of the Adomian-based approximations.Furthermore, the difference between the first- and second-order truncations is found to be negligible over the considered time interval, which suggests that even low-order Adomian expansions are sufficient to achieve reliable accuracy over short-time intervals. The results suggest that the Adomian Decomposition Method provides an effective way to approximate curvature-driven flows in short-time regimes.
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