Application of the Adomian Decomposition Method (ADM) to Solving the Systems of Partial Differential Equations

Justin Mouyedo Loufouilou, J. B. Yindoula, Gabriel Bissanga
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引用次数: 1

Abstract

Solving systems of partial differential equations (linear or nonlinear) with dirchelet boundary conditions has rarely made use of the Adomian decompositional method. The aim of this paper is to obtain the exact solution of some systems of linear and nonlinear partial differential equations using the adomian decomposition method.After having generated the basic principles of the general theory of this method, five systems of equations are solved, after calculation of the algorithm.Our results suggest that the use of the adomian method to solve systems of partial differential equations is efficient.However, further research should study other systems of linear or nonlinear partial differential equations to better understand the problem of uniqueness of solutions and boundary conditions.
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Adomian分解法在求解偏微分方程组中的应用
求解具有直切边界条件的偏微分方程(线性或非线性)系统很少使用Adomian分解方法。本文的目的是利用adomian分解方法,求得一类线性和非线性偏微分方程组的精确解。在推导出该方法一般理论的基本原理后,求解了五个方程组,并对算法进行了计算。我们的结果表明,使用adomian方法求解偏微分方程组是有效的。但是,为了更好地理解解的唯一性和边界条件的唯一性问题,需要进一步研究其他线性或非线性偏微分方程组。
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