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.

【摘要】 求解微分方程是物理学家的核心研究任务之一。就此而言，已知的求解方法越丰富，可被分析与阐释的问题范畴便越广阔。在各类微分方程中，非线性方程求解复杂度最高，且频繁出现于自然现象的建模描述之中。基于此，本文介绍了阿多米安分解法（Adomian Decomposition Method）——一种被广泛用于求解非线性微分方程的解析方法。为验证该方法的适用性，本文选取了若干线性与非线性算例进行演示，具体包括：考虑空气阻力的粒子自由下落运动、单摆运动，以及一维非均匀输运波动方程。