Solving Fourth-Order Lane-Emden-Fowler Equation by the New Modified Adomian Decomposition Method

This study explores the solutions of fourth-order Lane–Emden–Fowler (LEF) equations by employing a refined Modified Adomian Decomposition Method (MADM). We introduce a novel framework that features seven specialized differential operators, specifically developed and utilized to analyze the equations under specific initial and boundary conditions. Our findings demonstrate that the solutions derived from this approach not only effectively converge to the exact solutions but also offer unparalleled accuracy and reliability. A key strength of this methodology lies in its exceptional flexibility; solutions can be accurately obtained by applying at least one of these newly developed operators. This work significantly enhances our comprehension of these intricate equations and highlights the remarkable efficacy of the MADM in yielding precise solutions across diverse scenarios, thereby establishing a robust and versatile analytical tool