Evaluating Various Methods for Solving Third-Order Ordinary Differential Equations

Abstract

Adomian decomposition and Laplace transform methods (ADM & LTM) each have established roles in the mathematical toolkit for differential equations. The ADM is known for its iterative approach, breaking down complex differential equations into simpler, more manageable parts, which is especially useful for nonlinear problems. On the other hand, the Laplace transform method simplifies linear ordinary differential equations (ODEs) with constant coefficients by converting them into algebraic equations, facilitating easier solutions through algebraic manipulation.