In this study, we investigate third-order Emden-Fowler equations using the modified Adomian Decomposition Method (MADM). Six operators tailored to this framework are introduced and applied to analyze the equations under specific initial and boundary conditions. The results demonstrate that the solutions obtained via the modified Adomian Decomposition Method converge effectively to the exact solutions of the third-order Emden-Fowler equations. This work not only enhances the understanding of these complex equations but also highlights the effectiveness of the MADM in producing accurate solutions under varying conditions.
Dabwan et al. (Sun,) studied this question.