An Analytical Technique on Numerical Solutions for EFKs of Fourth Order and Higher (Journal of Nonlinear Modeling and Analysis, 2025)
This study introduces an advanced analytical technique for solving the fourth-order Extended Fisher-Kolmogorov (EFK) equation, focusingon the application of Adomian decomposition methods (ADM) and modifiedAdomian decomposition methods (MADM) . The research outlines a systematic approach to deriving numerical solutions, facilitating the characterizationand 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 solutionswhile addressing challenges inherent in higher-order differential equations.