Numerical solution of the coupled Lane–Emden–Fowler type equation using the variational iteration method and the Adomian polynomial

In this article, we introduce an efficient numerical approach for finding the numerical solution for coupled Lane–Emden–Fower type equations using the variational iteration method combined with the Adomian polynomial. The convergence analysis of the proposed approach is investigated under very general conditions. A couple of numerical examples are included and contrasted with the existing methods (Singh et al., 2021;Sinha et al., 2023;Duan et al., 2015) and the exact solution to check the robustness and effectiveness of the proposed approach. The present method shows faster convergence, computational efficiency, time efficiency and simplicity of implementation.