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A convenient computational form for the Adomian polynomials. (English) Zbl 0552.60061
Recent important generalizations by G. Adomian [Stochastic systems (1983; Zbl 0523.60056)] have extended the scope of his decomposition method for nonlinear stochastic operator equations (see also iterative method, inverse operator method, symmetrized method, or stochastic Green’s function method) very considerably so that they are now applicable to differential, partial differential, delay, and coupled equations which may be strongly nonlinear and/or strongly stochastic (or linear or deterministic as subcases). Thus, for equations modeling physical problems, solutions are obtained rapidly, easily, and accurately. The methodology involves an analytic parametrization in which certain polynomials $$A_ n$$, dependent on the nonlinearity, are derived. This paper establishes simple symmetry rules which yield Adomian’s polynomials quickly to high orders.

##### MSC:
 60H25 Random operators and equations (aspects of stochastic analysis)
##### Keywords:
inverse operator method; stochastic Green’s function
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