| dbo:abstract |
The Adomian decomposition method (ADM) is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The method was developed from the 1970s to the 1990s by George Adomian, chair of the Center for Applied Mathematics at the University of Georgia. It is further extensible to stochastic systems by using the Ito integral. The aim of this method is towards a unified theory for the solution of partial differential equations (PDE); an aim which has been superseded by the more general theory of the homotopy analysis method. The crucial aspect of the method is employment of the "Adomian polynomials" which allow for solution convergence of the nonlinear portion of the equation, without simply linearizing the system. These polynomials mathematically generalize to a Maclaurin series about an arbitrary external parameter; which gives the solution method more flexibility than direct Taylor series expansion. (en) La décomposition d'Adomian est une méthode semi-analytique de résolution d'équations différentielles développée par le mathématicien américain (en) durant la seconde partie du XXe siècle. On rencontre fréquemment l'utilisation d'ADM pour Adomian Decomposition Method. (fr) 阿多米安分解法（Adomian decomposition method，简称：ADM法），是1989年美国籍阿马尼亚数学家George Adomian创建的近似分解法，用以求解非线性偏微分方程 将非线性偏微分方程写成如下形式： 其中 L、R为线性偏微分算子，NL为非线性项。 将反算子. 用于上式 . 得 . 令方程的解u（x,t) 为： 非线性项 NL（u）= 其中 由此得 近似解= (zh) |
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| rdfs:comment |
La décomposition d'Adomian est une méthode semi-analytique de résolution d'équations différentielles développée par le mathématicien américain (en) durant la seconde partie du XXe siècle. On rencontre fréquemment l'utilisation d'ADM pour Adomian Decomposition Method. (fr) 阿多米安分解法（Adomian decomposition method，简称：ADM法），是1989年美国籍阿马尼亚数学家George Adomian创建的近似分解法，用以求解非线性偏微分方程 将非线性偏微分方程写成如下形式： 其中 L、R为线性偏微分算子，NL为非线性项。 将反算子. 用于上式 . 得 . 令方程的解u（x,t) 为： 非线性项 NL（u）= 其中 由此得 近似解= (zh) The Adomian decomposition method (ADM) is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The method was developed from the 1970s to the 1990s by George Adomian, chair of the Center for Applied Mathematics at the University of Georgia. It is further extensible to stochastic systems by using the Ito integral. The aim of this method is towards a unified theory for the solution of partial differential equations (PDE); an aim which has been superseded by the more general theory of the homotopy analysis method. The crucial aspect of the method is employment of the "Adomian polynomials" which allow for solution convergence of the nonlinear portion of the equation, without simply linearizing the system. These polynomials mathematically generalize to a M (en) |
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Adomian decomposition method (en) Décomposition d'Adomian (fr) 阿多米安分解法 (zh) |
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