A probabilistic approach to Adomian polynomials
A probabilistic approach to Adomian polynomials
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DOI：
10.1080/07362994.2020.1755312
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发表时间：
2020-05
影响因子：
1.3
通讯作者：
P. Vellaisamy;F. Viens
中科院分区：
文献类型：
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作者：
P. Vellaisamy;F. Viens
Adomian分解法（ADM）是求解若干非线性泛函方程和一类初值/边值问题的有力工具。本文讨论了一种计算Adomian多项式的概率方法，它是Adomian多项式的主要部分。我们给出了单变量和多变量情况下的Adomian多项式的概率解释。我们得到了计算AP的一些新的递归关系。讨论了一些合适的例子，表明概率方法计算AP比分析或组合方法简单得多。
Abstract The Adomian decomposition method (ADM) is a powerful tool to solve several nonlinear functional equations and a large class of initial/boundary value problems. In this paper, we discuss a probabilistic approach to compute the Adomian polynomials (AP’s), which is the main part of the ADM. We provide a probabilistic interpretation for the AP’s, both for the one-variable and the multivariable case. We derive some new recurrence relations for the computation AP’s. Some suitable examples are discussed to show that the probabilistic approach to compute the AP’s is much simpler than the analytical or combinatorial approach.