Partial Differential Equations (PDEs) play a crucial role in the modeling of various physical phenomena. Exact solutions to PDEs are rare, especially for nonlinear equations. Semi-analytic methods such as the Adomian Decomposition Method (ADM), the Homotopy Analysis Method (HAM), and the Laplace Adomian Decomposition Method (LADM) provide effective alternatives for approximate analytical solutions. This review discusses the principles and methodologies of these three methods in detail and demonstrates each with an illustrative example. MSC 2010: 47H08, 47H09, Keywords: Adomian Decomposition Method, Homotopy Analysis Method, Laplace Decomposition Method.
Malge et al. (Thu,) studied this question.