Advanced Variational Iteration Method to Solve Two Different Models of Third‐Order Nonlinear Emden–Fowler‐Type Equations

ABSTRACT In this research, we propose an advanced variational iteration method by employing the Adomian polynomials with the variational iteration method to solve the system of third‐order nonlinear Emden–Fowler‐type equations arise in several applications. The third‐order nonlinear Emden–Fowler‐type equations have singularity at origin and are characterized by two models, with the shaped factor appearing two times in the first model and once in the other model. The proposed method overcomes the singularity at the origin and handles both models with different‐shaped factors. The convergence study of the proposed method for both models is also discussed in Banach space. Five models of interest are provided to test the validity and efficiency of the proposed method. The investigations confirm that the proposed method is able to solve complex problems in a few iterations with less computational time.