The Solution of Third Order Ordinary Differential Equations using Adomian Decomposition Method and Variational Iteration Method

Abstract

Solving ordinary differential equations is crucial in physics, engineering, and mathematics. Adomian decomposition method and variational iteration method are two of many methods in solving ordinary differential equations. Both techniques involve constructing the required iterative or recurrence formulas based on the equation under consideration and additional requirements, allowing the identification of succeeding iterations of a series or sequence approximately matching to solve the third order ordinary differential equations. In this study, adomian decomposition method and variational iteration method will be used in solving homogenous and nonhomogeneous third order ordinary differential equations and analysis on method of solutions will be discussed. Overall, it is identified that both methods are efficient in solving linear third order ordinary differential equations.