Solving Higher Order Ordinary Differential Equations in Physics: A New Modified Adomian Decomposition Method Approach to MHD Flows, Elastic Beam, and Sixth-Order Boundary value problem

The study presents a novel approach for solving highe-order ordinary differential equations (ODEs) prevalent in various physics applications, specifically through a modified Adomian Decomposition Method (ADM). This method enhances the traditional ADM by introducing specific modifications that improve its convergence and applicability to complex problems. The research focuses on three primary areas: magnetohydrodynamic (MHD) flows, the dynamics of elastic beams, and sixth-order boundary value problems. The proposed method demonstrates significant effectiveness in deriving analytical solutions that can accurately predict physical behaviors in these domains. By applying the modified ADM, the study not only addresses the challenges associated with higher order ODEs but also offers practical solutions for engineers and physicists working with intricate modeling scenarios. The results indicate that this method provides an efficient and reliable framework for analyzing and solving complex differential equations in the field of physics and engineering.