Solving differential equations using adomian decomposition method

Abstract

Searching for solution of a differential equation can be one of the main tasks of a physicist. In this sense, the greater the number of known solution methods, the wider the variety of problems that can be analyzed and understood. Among the differential equations, the non-linear equations are the ones with the greatest resolution complexity and are routinely present in the description of natural phenomena. In this perspective, this work presents an introduction to the Adomian Decomposition Method, which is an analytical method vastly used to address non-linear differential equations. To exemplify the applicability of the Adomian method, some linear and non-linear examples are treated, namely: free fall of a particle under air resistance, simple gravity pendulum and a one-dimensional non-uniform transport wave equation.