Modified Adomian Decomposition Method for Solving SingularDifferential Equation of Lane-Emden Type
DOI:
https://doi.org/10.14419/1yf6t398الكلمات المفتاحية:
Modified Adomian Method, Numerical Method, Singular Equations, Lane-Emden Equations, linear and Nonlinear Equationsالملخص
This paper presents a novel adaptation of the Adomian Decomposition Method specifically designed to solve Lane-Emden equations moreeffectively. Unlike traditional approaches, our method eliminates the need for integral operators, a common source of computationalcomplexity in previous versions of the Adomian method. By relying exclusively on differential operators, we simplify the problem-solvingprocess, allowing for direct differentiation without the approximation challenges associated with integral coefficients. This enhancement notonly streamlines the computational workload but also significantly improves both the accuracy and efficiency of solutions to Lane-Emdenequations. We provide rigorous demonstrations of our method through various examples, illustrating marked advantages over conventionaltechniques in terms of convergence rates and computational simplicity. The unique contribution of this work lies in its potential to inspirefurther research and applications across diverse fields that utilize higher-order differential equations.
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