<![CDATA[This study introduces a novel analytical technique that integrates the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) to solve nonlinear differential equations, with particular emphasis on logistic growth models. The proposed hybrid method leverages the recursive decomposition mechanism of ADM alongside the correction functional framework of VIM to improve both the convergence rate and the accuracy of the solutions. To assess its effectiveness, the method is applied to selected cases of the logistic differential equation. The resulting approximate solutions exhibit strong agreement with known exact solutions, demonstrating the method's reliability and potential in addressing complex nonlinear problems in applied mathematics. This approach offers a robust alternative for researchers and practitioners seeking efficient analytical tools for nonlinear modeling.]]>
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