(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
This study introduces an advanced analytical technique for solving the fourth-order Extended Fisher-Kolmogorov (EFK) equation, focusing on the application of Adomian decomposition methods (ADM) and modified Adomian decomposition methods (MADM) . The research outlines a systematic approach to deriving numerical solutions, facilitating the characterization and understanding of complex dynamics associated with the EFK equation. Additionally, the technique is generalized to higher-order extensions, enhancing its applicability in modeling various physical phenomena. The results illustrate the effectiveness of the proposed methods in achieving accurate solutions while addressing challenges inherent in higher-order differential equations.