Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations

Partial Differential Equations (PDE) help model problems in science and engineering, given their abilities to capture complex phenomena compared to Ordinary Differential Equations. This paper aims to investigate two semi-analytical techniques called the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM), how these methods can be used in practice, and to make a comparative study of the two methods for solving linear and nonlinear PDEs. The efficiency of ADM and VIM is assessed by comparing their errors relative to the exact solutions of the examined numerical experiments. The results obtained from the numerical experiments revealed that ADM proved to be a more efficient and accurate method for solving PDEs than VIM.