Abstract: The Abaoub-Shkheam Decomposition Method (QDM) is employed in this paper to solve nonlinear initial value problems of second order. Adomian polynomial is used to decompose nonlinear functions that exist in a given equation. We are using this method (QDM) to find the exact solution of different types of non-linear ordinary differential equations, which is based on the Abaoub Shkheam transform method (QTM) and the Adomian Decomposition Method (ADM). An example is provided to demonstrate the efficacy of this approach.

Keywords: Ordinary differential equations, Abaoub Shkheam transform, Adomian Decomposition Methodise.

| DOI: 10.17148/IARJSET.2024.111202